量子密钥分发为什么能保证密钥"不可窃听"？
Why does quantum key distribution make an eavesdropping-proof key possible?
量子密钥分发用单光子来传送密钥：一个光子只能携带一个量子比特，窃听者想复制或测量它，就必须先与它发生相互作用，而这必然改变光子的量子态。收发双方核对部分样本时，任何窃听痕迹都会暴露，被污染的密钥随即丢弃重发，量子不可克隆定理保证了这一安全性。我国的"墨子号"卫星已经在千公里尺度上实现了星地之间的量子密钥分发。
Quantum key distribution sends the key one photon at a time: a photon carries a single qubit, and an eavesdropper who tries to copy or measure it must interact with it, inevitably disturbing its quantum state. When the two parties compare test samples, any interception leaves a detectable trace, so the compromised key is discarded and re-sent — guaranteed by the no-cloning theorem. China's Micius satellite has demonstrated satellite-to-ground key distribution across thousands of kilometers.
难度 专业 · 适合 高中(15-18)
CC BY 4.0 · 来源待核验 · Source pending review
来源 · Source
出处备注：此条未指向带版次的可引用著作（通识性内容、机构文件或未展开的英文书名），本库不提供独立书目出处；如需精确引用，需由编辑补全具体篇目与版次。
中国科学院（量子通信实验）
Chinese Academy of Sciences (quantum communication experiments)
#量子密钥分发 #量子比特 #不可克隆
量子叠加态如何被数学描述？
How is a quantum superposition described mathematically?
一个量子态用希尔伯特空间中的态矢量表示，叠加态是多个基矢量的线性组合：|ψ⟩=α|0⟩+β|1⟩。测量时以|α|²、|β|²的概率得到对应本征态。这种线性结构是量子并行与干涉的根源。
A quantum state is a state vector in Hilbert space, and a superposition is a linear combination of basis vectors: |ψ⟩=α|0⟩+β|1⟩. Upon measurement the outcome is an eigenstate with probabilities |α|² and |β|². This linear structure underlies quantum parallelism and interference.
难度 专业 · 适合 高中(15-18)
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
曾谨言,《量子力学 卷I》,科学出版社,2013
Zeng Jinyan, Quantum Mechanics Vol.I, Science Press, 2013
独立核验依据 · Independent verification: 核验依据 2 DOUBAN ISBN 标识 9787030387226（按标识回读: 量子力学 卷1）
#叠加态 #希尔伯特空间 #态矢量
隧道二极管为什么能利用量子隧穿做出经典器件做不到的高速开关？
How can a tunnel diode use quantum tunneling to switch faster than classical devices allow?
在重掺杂的 PN 结里，能带严重交叠，载流子能借量子隧穿直接穿过势垒，形成随电压先升后降的负阻区。这种负微分电阻使器件可在极短的时间内翻转状态，因此被广泛用于微波和超高速电路。它本质上是量子效应在半导体里的直接应用。
In a heavily doped p–n junction the bands overlap enough that carriers tunnel straight through the barrier, producing a negative-resistance region where current first rises then falls with voltage. This negative differential resistance lets the device switch state extremely fast, so it is used in microwave and ultra-high-speed circuits. It is a direct application of quantum tunneling in semiconductors.
难度 专业 · 适合 高中(15-18)
CC BY 4.0 · 来源待核验 · Source pending review
来源 · Source
出处备注：著录含书名，但缺版次 / 出版社 / 年份中的一部分，需编辑补全后才能做独立比对。
L. Esaki,《New Phenomenon in Narrow Germanium p-n Junctions》,Physical Review 109,603(1958)
L. Esaki, 'New Phenomenon in Narrow Germanium p-n Junctions', Physical Review 109, 603 (1958)
#量子隧穿 #隧道二极管 #负阻
电子的“自旋”是像地球那样自转吗？
Is an electron's spin like Earth spinning on its axis?
不是。自旋是电子固有的内禀角动量，没有经典对应物，不能理解为小球的自转。它取固定量子值（±ℏ/2），是粒子的基本属性。
No. Spin is an intrinsic angular momentum with no classical counterpart, not a tiny ball turning. It takes fixed quantum values (±ℏ/2) and is a basic property of the particle.
难度 专业 · 适合 高中(15-18)
CC BY 4.0 · 已核验 · Verified 2026-10-03 · 2 条独立证据
来源 · Source
《费曼物理学讲义》
The Feynman Lectures on Physics
独立核验依据 · Independent verification: 核验依据 2 ISBN 978-0-7382-0298-3 (2006 Pearson 版，原始版为1963-65 Addis
#自旋 #内禀角动量 #量子数
太阳核心只有1500万度，质子凭什么越过静电斥力发生聚变？
The Sun's core is only about 15 million degrees — how do protons get past electrostatic repulsion to fuse?
按经典物理，两个质子必须爬过库仑势垒才能靠近到足以聚变，而1500万度对应的平均动能远远不够。量子隧穿解决了这个矛盾：即使能量低于势垒，质子的波函数也会渗过势垒，让它以小概率直接出现在近距离处。单个事件概率极低，但太阳里质子数量极其庞大，每秒仍有海量聚变发生。可以说，没有量子隧穿，太阳根本燃不起来。
Classically, two protons must climb over the Coulomb barrier to get close enough to fuse, and 15 million degrees provides far too little energy on average. Quantum tunneling rescues the Sun: even below the barrier, a proton's wavefunction leaks through it, so the proton occasionally appears at fusion distance. Each individual event is extraordinarily rare, but the Sun holds so many protons that fusion proceeds at a colossal rate. Without tunneling, the Sun simply could not ignite.
难度 专业 · 适合 高中(15-18)
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
Griffiths & Schroeter,《Introduction to Quantum Mechanics》第3版,Cambridge University Press,2018
D. J. Griffiths and D. F. Schroeter, Introduction to Quantum Mechanics, 3rd ed., Cambridge University Press, 2018
独立核验依据 · Independent verification: 核验依据 2 ARCHIVE 标识 introduction-to-quantum-mechanics_202510：Intr
#量子隧穿 #库仑势垒 #核聚变
做贝尔实验检验量子纠缠时，那一对对“纠缠光子”通常是从哪儿来的？
In Bell-test experiments on quantum entanglement, where do the pairs of 'entangled photons' usually come from?
如今的标准做法是让泵浦光子在非线性晶体（如 BBO）中发生自发参量下转换，一个高频光子分裂为两个低频光子，二者能量、动量互补，可制备成偏振纠缠态。但阿斯佩 1982 年的经典实验用的并不是这种源，而是钙原子级联辐射产生的光子对。参量下转换自 1988 年前后才逐步取代原子级联，1995 年 Kwiat 等人的高亮度纠缠源使贝尔检验效率大幅提升。
Today's standard source is spontaneous parametric down-conversion in a nonlinear crystal such as BBO, where one pump photon splits into two lower-frequency photons that are complementary in energy and momentum and can be prepared in a polarization-entangled state. Aspect's classic 1982 experiment, however, did not use this source: its photon pairs came from a calcium atomic cascade. Down-conversion only replaced atomic cascades from around 1988, and the bright entangled source of Kwiat et al. in 1995 sharply improved the efficiency of Bell tests.
难度 专业 · 适合 高中(15-18)
CC BY 4.0 · 已核验 · Verified 2026-10-04
来源 · Source
P. G. Kwiat et al.,《New High-Intensity Source of Polarization-Entangled Photon Pairs》,Phys. Rev. Lett. 75,4337(1995)
P. G. Kwiat et al., 'New High-Intensity Source of Polarization-Entangled Photon Pairs', Phys. Rev. Lett. 75, 4337 (1995)
独立核验依据 · Independent verification: 核验依据 1 DOI 10.1103/physrevlett.75.4337
#参量下转换 #纠缠光子 #贝尔实验
海森堡绘景与薛定谔绘景有何不同？
How do the Heisenberg and Schrödinger pictures differ?
在薛定谔绘景中态矢量随时间演化，而算符固定；在海森堡绘景中态固定，算符随时间演化。两者通过幺正变换相联系，对物理预言完全一致。选择哪种只是计算方便的约定。
In the Schrödinger picture the state vector evolves in time while operators are fixed; in the Heisenberg picture the state is fixed and operators evolve. They are linked by a unitary transformation and make identical physical predictions. The choice is merely a matter of calculational convenience.
难度 专业 · 适合 初中(12-15)
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
曾谨言,《量子力学 卷I》,科学出版社,2013
Zeng Jinyan, Quantum Mechanics Vol.I, Science Press, 2013
独立核验依据 · Independent verification: 核验依据 2 DOUBAN ISBN 标识 9787030387226（按标识回读: 量子力学 卷1）
#薛定谔绘景 #海森堡绘景 #幺正
扫描隧道显微镜是怎样"看见"单个原子的？
How does a scanning tunneling microscope "see" individual atoms?
它利用量子隧穿效应：当极细的金属针尖贴近导电样品表面时，电子能"穿过"针尖与样品之间的真空缝隙，形成微弱电流。隧穿电流对间距极其敏感，针尖与样品的距离每改变一个原子直径，电流就变化约十倍。通过逐点扫描并记录针尖的升降，仪器就能把样品表面的原子排列还原成图像。宾尼希与罗雷尔因此获得1986年诺贝尔物理学奖。
It exploits quantum tunneling: when an atomically sharp metal tip approaches a conducting surface, electrons tunnel across the vacuum gap and form a tiny current. This current is exquisitely sensitive — it changes about tenfold for every change in separation of one atomic diameter. Scanning point by point and recording the tip height reconstructs the surface's atomic arrangement as an image. Binnig and Rohrer won the 1986 Nobel Prize in Physics for this work.
难度 专业 · 适合 高中(15-18)
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
曾谨言,《量子力学 卷I》,科学出版社,2013
Zeng Jinyan, Quantum Mechanics Vol.I, Science Press, 2013
独立核验依据 · Independent verification: 核验依据 2 DOUBAN ISBN 标识 9787030387226（按标识回读: 量子力学 卷1）
#量子隧穿 #扫描隧道显微镜 #纳米
普朗克的「量子假说」是怎样诞生的，解决了什么危机？
How did Planck's quantum hypothesis arise, and what crisis did it resolve?
19世纪末，用经典物理推算「黑体辐射」在高频段会发散（紫外灾难），与实验完全不符。普朗克1900年为拟合数据，大胆假设能量不是连续的，而是以 E = hν 的最小单位（量子）一份份发射吸收，由此得到与实验完美吻合的曲线。这开创了量子论，h 也成为自然界的基本常数。
In the late 19th century classical physics predicted blackbody radiation would diverge at high frequencies (the ultraviolet catastrophe), contradicting experiment. To fit the data, Planck proposed in 1900 that energy is not continuous but emitted and absorbed in minimal quanta E = hν, yielding a curve that matched perfectly. This founded quantum theory and made h a fundamental constant.
难度 专业 · 适合 高中(15-18)
CC BY 4.0 · 已核验 · Verified 2026-11-03
来源 · Source
M. 普朗克 1900 年黑体辐射论文；《量子理论史》（范德瓦尔登编）
M. Planck (1900) blackbody radiation paper; 'Sources of Quantum Mechanics' (van der Waerden, ed.)
独立核验依据 · Independent verification: 核验依据 1 OPENLIBRARY 标识 /works/OL19336886W：Sources of Quantum Mec
#普朗克量子 #黑体辐射 #紫外灾难
什么是波函数坍缩？
What is wavefunction collapse?
在量子力学中，系统的状态由波函数描述，它给出各结果的概率。进行测量时，波函数会从多个可能结果的概率分布突然变为某个确定结果，称为波函数坍缩。
In quantum mechanics a system's state is described by a wavefunction giving probabilities of outcomes. Upon measurement, the wavefunction suddenly changes from a spread of possibilities to one definite result, called collapse.
难度 专业 · 适合 高中(15-18)
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
曾谨言,《量子力学 卷I》,科学出版社,2013
Zeng Jinyan, Quantum Mechanics Vol.I, Science Press, 2013
独立核验依据 · Independent verification: 核验依据 2 DOUBAN ISBN 标识 9787030387226（按标识回读: 量子力学 卷1）
#波函数 #坍缩 #测量
量子态在测量之前由薛定谔方程确定地演化，为什么一测量却表现出不可逆的“坍缩”？
A quantum state evolves deterministically by Schrödinger's equation before measurement, so why does measurement bring an irreversible 'collapse'?
冯·诺依曼把量子过程分成两段：测量前的幺正演化连续且可逆，测量时系统与宏观仪器的纠缠使叠加在可观测结果上“退相干”，表现为不可逆的投影坍缩。测量问题至今没有完全定论，但它清楚区分了演化与读取两个环节。
Von Neumann split quantum processes into two parts: a unitary, continuous, reversible evolution before measurement, and an irreversible projection at measurement, where entanglement with a macroscopic apparatus decoheres the superposition. The measurement problem remains unsettled, but it clearly separates evolution from readout.
难度 专业 · 适合 高中(15-18)
CC BY 4.0 · 已核验 · Verified 2026-11-03结论有争议 · Contested
来源 · Source
J. von Neumann,《Mathematical Foundations of Quantum Mechanics》(英译本,Princeton Univ. Press,1955;德文原版 Springer,1932),第6章(测量过程)
J. von Neumann, 'Mathematical Foundations of Quantum Mechanics' (English transl., Princeton Univ. Press, 1955; German original Springer, 1932), Ch.6 (The Measuring Process)
独立核验依据 · Independent verification: 核验依据 1 OPENLIBRARY 标识 /works/OL1204967W：Mathematical foundation
#测量问题 #波函数坍缩 #退相干
量子隧穿为什么允许粒子穿过本应不可逾越的势垒？
Why does quantum tunneling let particles cross classically forbidden barriers?
在量子力学里粒子的位置由波函数描述，而波函数在势垒内部并不立即降为零，因此粒子有一定概率出现在壁垒另一侧。Gurney 与 Condon 在 1928 年用此解释原子核的 α 衰变。
In quantum mechanics a particle is described by a wavefunction that does not instantly drop to zero inside a barrier, so there is a finite probability of finding it on the far side. Gurney and Condon used this in 1928 to explain alpha decay of nuclei.
难度 专业 · 适合 高中(15-18)
CC BY 4.0 · 已核验 · Verified 2026-11-03
来源 · Source
Griffiths《量子力学导论》；Gurney 与 Condon 1928 年论文
Griffiths, Introduction to Quantum Mechanics; Gurney & Condon (1928)
独立核验依据 · Independent verification: 核验依据 1 ARCHIVE 标识 introduction-to-quantum-mechanics_202510：Intr
#量子隧穿 #波函数 #α衰变
量子计算机凭什么可能比普通计算机快得多？
Why might a quantum computer be far faster than an ordinary one?
普通比特非0即1，量子比特（qubit）可处于0和1的叠加，还能与别的量子比特纠缠，使 n 个比特同时代表 2^n 种组合，对特定问题（如大数分解、搜索）实现并行式的指数加速。肖尔1994年给出分解大数的量子算法，理论上能威胁现有公钥加密。难点在于量子态极易受环境干扰（退相干），需极低温与纠错。
A classical bit is 0 or 1, but a qubit can be a superposition of both and entangle with others, so n qubits represent 2^n combinations at once—enabling exponential speedups for tasks like factoring or searching. Shor's 1994 algorithm could factor large numbers and threaten public-key encryption. The catch is that quantum states decohere easily, demanding extreme cold and error correction.
难度 专业 · 适合 高中(15-18)
CC BY 4.0 · 已核验 · Verified 2026-10-04
来源 · Source
P. 肖尔 1994 年量子分解算法（SIAM J. Computing）；尼尔森与庄《量子计算与量子信息》
P. Shor (1994) quantum factoring algorithm, SIAM J. Comput.; Nielsen & Chuang, 'Quantum Computation and Quantum Information'
独立核验依据 · Independent verification: 核验依据 1 ISBN 9780521635035 (2016)
#量子计算 #量子比特 #叠加与纠缠
晶体管凭什么成为现代电子设备的"心脏"？
Why is the transistor called the heart of modern electronic devices?
晶体管用很小的电压或电流去控制一条大得多的电路，从而完成放大与开关两大功能。双极型晶体管由三层半导体构成，基极电流的微小变化能控制集电极的大电流，信号因此被放大；场效应晶体管则靠栅极电压调制沟道的导电能力。计算机芯片里数十亿个晶体管相互协作完成运算，放大器、振荡器和存储器全都建立在它的基础上。
A transistor uses a small voltage or current to control a much larger current, giving it the twin jobs of amplification and switching. A bipolar transistor stacks three semiconductor layers: a tiny base current governs a large collector current, amplifying the signal, while a field-effect transistor's gate voltage modulates how well its channel conducts. Billions of transistors cooperate inside a computer chip to compute, and amplifiers, oscillators and memory all rest on them.
难度 专业 · 适合 高中(15-18)
CC BY 4.0 · 已核验 · Verified 2026-10-03
来源 · Source
S. M. Sze 与 Kwok K. Ng 著《Physics of Semiconductor Devices》（半导体器件物理）
S. M. Sze & Kwok K. Ng, Physics of Semiconductor Devices
独立核验依据 · Independent verification: 核验依据 1 ISBN 9780470068328
#晶体管 #放大 #集成电路
诺特定理如何把对称性与守恒律联系起来？
How does Noether's theorem link symmetry and conservation laws?
诺特定理证明：每一个连续的对称性都对应一个守恒量。时间平移对称对应能量守恒，空间平移对称对应动量守恒，空间旋转对称对应角动量守恒。它揭示了守恒定律的深层几何来源。
Noether's theorem proves that every continuous symmetry corresponds to a conserved quantity. Time-translation symmetry gives energy conservation, spatial translation gives momentum conservation, and rotational symmetry gives angular momentum conservation. It reveals the deep geometric origin of conservation laws.
难度 专业 · 适合 高中(15-18)
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
曾谨言,《量子力学 卷I》,科学出版社,2013
Zeng Jinyan, Quantum Mechanics Vol.I, Science Press, 2013
独立核验依据 · Independent verification: 核验依据 2 DOUBAN ISBN 标识 9787030387226（按标识回读: 量子力学 卷1）
#诺特定理 #对称性 #守恒律
量子霍尔效应为什么能极其精确地定义电阻？
Why can the quantum Hall effect define resistance with extreme precision?
在强磁场和低温下，二维电子气的霍尔电阻只取 h/(ne²) 这样的量子化平台，只依赖基本常数。它因此被用来定义电阻单位“欧姆”。
In strong magnetic fields and at low temperature, a 2D electron gas shows Hall resistance pinned to quantized plateaus h/(ne²), depending only on fundamental constants. It is used to define the ohm.
难度 专业 · 适合 高中(15-18)
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
曾谨言,《量子力学 卷I》,科学出版社,2013
Zeng Jinyan, Quantum Mechanics Vol.I, Science Press, 2013
独立核验依据 · Independent verification: 核验依据 2 DOUBAN ISBN 标识 9787030387226（按标识回读: 量子力学 卷1）
#量子霍尔 #电阻标准 #二维电子气
量子场论如何把量子力学与相对论统一起来？
How does quantum field theory unify quantum mechanics and relativity?
量子场论把粒子视为充满时空的场的激发，场算符按相对论协变方式演化，自然容纳了粒子的产生与湮灭。它在保持洛伦兹协变性下完成量子化，并成为描述基本粒子相互作用的标准模型基础。
Quantum field theory treats particles as excitations of fields filling spacetime, with field operators evolving in a relativistically covariant way, naturally allowing particle creation and annihilation. It quantizes while preserving Lorentz covariance and forms the basis of the Standard Model of particle interactions.
难度 专业 · 适合 高中(15-18)
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
曾谨言,《量子力学 卷I》,科学出版社,2013
Zeng Jinyan, Quantum Mechanics Vol.I, Science Press, 2013
独立核验依据 · Independent verification: 核验依据 2 DOUBAN ISBN 标识 9787030387226（按标识回读: 量子力学 卷1）
#量子场论 #场 #相对论协变
海森堡不确定性原理说我们不能同时知道什么？
What can't we know at the same time, per Heisenberg's uncertainty principle?
它说粒子的位置和动量无法同时被任意精确测定，乘积存在下限（Δx·Δp ≥ ℏ/2）。这不是仪器不够好，而是量子世界本身的限制。
It says a particle's position and momentum cannot both be known arbitrarily precisely; their uncertainties satisfy Δx·Δp ≥ ℏ/2. This is not a flaw of instruments but a built-in limit of the quantum world.
难度 专业 · 适合 高中(15-18)
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
Griffiths & Schroeter,《Introduction to Quantum Mechanics》第3版,Cambridge University Press,2018
D. J. Griffiths and D. F. Schroeter, Introduction to Quantum Mechanics, 3rd ed., Cambridge University Press, 2018
独立核验依据 · Independent verification: 核验依据 2 ARCHIVE 标识 introduction-to-quantum-mechanics_202510：Intr
#不确定性原理 #海森堡 #量子
为什么电子、质子这类费米子彼此“排斥”不能同态，而光子这类玻色子却可以无数个挤进同一状态？
Why do fermions like electrons and protons refuse to share a state while bosons like photons can pile infinitely into the same one?
这是自旋–统计定理的结果：半整数自旋的费米子服从泡利不相容原理，同一量子态最多容纳一个。整数自旋的玻色子则不受此限，可以全部凝聚到同一最低能态，形成玻色–爱因斯坦凝聚。两种统计决定了物质结构与激光等截然不同的现象。
This follows from the spin–statistics theorem: half-integer-spin fermions obey the Pauli exclusion principle, so at most one can occupy a given state. Integer-spin bosons face no such limit and can all collapse into the same lowest state, as in a Bose–Einstein condensate. The two statistics underlie both matter structure and phenomena like lasers.
难度 专业 · 适合 高中(15-18)
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D. J. Griffiths,《Introduction to Quantum Mechanics》(第2版),第5章(全同粒子)
D. J. Griffiths, 'Introduction to Quantum Mechanics' (2nd ed.), Ch.5 (Identical particles)
#费米子 #玻色子 #自旋统计定理
玻色-爱因斯坦凝聚是什么，为什么要在极低温下才看得到？
What is a Bose–Einstein condensate, and why is extreme cold needed to see it?
当一种玻色子气体被冷却到纳开尔文量级，几乎所有原子都跌入同一个最低量子态，整体表现为一个宏观的、相干的量子波——这就是 BEC。温度越低，热运动越小，德布罗意波长越长，长到原子彼此重叠时才「凝聚」成一体。康奈尔、维曼与克特勒1995年首次实现，获2001年诺贝尔奖。
When a gas of bosons is cooled to nanokelvin temperatures, nearly all atoms drop into the same lowest quantum state and behave as one macroscopic coherent quantum wave—a BEC. Lower temperature means less thermal motion and longer de Broglie wavelengths, which overlap and 'condense' only when long enough. Cornell, Wieman, and Ketterle first achieved it in 1995, winning the 2001 Nobel Prize.
难度 专业 · 适合 高中(15-18)
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诺贝尔物理学奖 2001（康奈尔、维曼、克特勒，BEC）；《统计物理》（帕斯里亚）
Nobel Prize in Physics 2001 (Cornell, Wieman, Ketterle, BEC); Pathria, 'Statistical Mechanics'
独立核验依据 · Independent verification: 核验依据 1 OPENLIBRARY 标识 /works/OL1624664W：Statistical mechanics（首
#玻色-爱因斯坦凝聚 #玻色子 #宏观量子态
量子擦除实验里，为什么“抹掉”路径信息后，原本消失的干涉条纹又能重新出现——哪怕光子早已做出“选择”？
In a quantum eraser, why can erasing the path information bring back interference fringes that had vanished—even after the photon already 'chose'?
互补原理说，一旦能原则上知道光子走了哪条路，叠加就被破坏、干涉消失。量子擦除器通过把路径标记与另一自由度纠缠、再对标记做测量后筛选，等效地“销毁”了哪条路的信息，于是互补性恢复，筛选后的子集中干涉条纹重现。它凸显了“信息可及性”而非时间点决定干涉。
Complementarity says that once path information is in principle available, the superposition is destroyed and interference vanishes. A quantum eraser entangles the path marker with another degree of freedom and, by later measuring and sorting on the marker, effectively destroys which-path information, restoring complementarity so fringes reappear in the selected subset. It shows that accessibility of information, not the timing, decides interference.
难度 专业 · 适合 高中(15-18)
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T. J. Herzog et al.,《Complementarity and the Quantum Eraser》,Phys. Rev. Lett. 75,3034(1995)
T. J. Herzog et al., 'Complementarity and the Quantum Eraser', Phys. Rev. Lett. 75, 3034 (1995)
独立核验依据 · Independent verification: 核验依据 1 EUROPEPMC 标识 10059478：Complementarity and the quantum er
#量子擦除 #互补原理 #路径信息
波函数的概率诠释是怎样提出的？
How was the probabilistic interpretation of the wavefunction proposed?
玻恩提出，波函数的模平方给出在某处找到粒子的概率密度，而非粒子确定的轨迹。这一诠释把量子力学从决定论描述转为概率描述，成为哥本哈根诠释的核心。它至今仍是标准解释的基础。
Born proposed that the square modulus of the wavefunction gives the probability density of finding a particle at a location, rather than a definite trajectory. This shifted quantum mechanics from deterministic to probabilistic description and became the core of the Copenhagen interpretation. It remains the basis of the standard view.
难度 专业 · 适合 初中(12-15)
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
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曾谨言,《量子力学 卷I》,科学出版社,2013
Zeng Jinyan, Quantum Mechanics Vol.I, Science Press, 2013
独立核验依据 · Independent verification: 核验依据 2 DOUBAN ISBN 标识 9787030387226（按标识回读: 量子力学 卷1）
#波函数 #概率诠释 #玻恩
费曼路径积分如何重新表述量子力学？
How does Feynman's path integral reformulate quantum mechanics?
路径积分认为，粒子从一点到另一点不是走单一轨迹，而是遍历所有可能路径，每条路径贡献一个带相位的振幅e^{iS/ħ}，总和给出总概率幅。作用量S最小的经典路径在宏观极限下主导结果。它把量子规律表达为对历史的求和。
The path integral says a particle from one point to another does not follow a single trajectory but samples all possible paths, each contributing an amplitude e^{iS/ħ} with phase, and their sum gives the total probability amplitude. The classical path of least action dominates in the macroscopic limit. It expresses quantum law as a sum over histories.
难度 专业 · 适合 高中(15-18)
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
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曾谨言,《量子力学 卷I》,科学出版社,2013
Zeng Jinyan, Quantum Mechanics Vol.I, Science Press, 2013
独立核验依据 · Independent verification: 核验依据 2 DOUBAN ISBN 标识 9787030387226（按标识回读: 量子力学 卷1）
#路径积分 #费曼 #作用量
为什么电子能「穿墙」——隧穿效应，以及它怎么被用来看见原子？
Why can electrons 'tunnel through walls,' and how is this used to see atoms?
在量子力学里，粒子遇到比自身能量还高的势垒时，波函数仍会渗入并在另一侧以一定概率重新出现，这叫隧穿。扫描隧道显微镜（STM）把极细针尖凑近样品表面，靠针尖与表面间的隧穿电流随距离指数变化，逐点扫描就能「摸」出单个原子的起伏。宾宁与罗雷尔1981年发明，获1986年诺贝尔奖。
In quantum mechanics a particle hitting a barrier higher than its energy still has a wavefunction that leaks through and re-emerges on the far side with some probability—tunneling. A scanning tunneling microscope (STM) brings a sharp tip near a surface; the tunneling current varies exponentially with distance, so scanning maps individual atomic bumps. Binnig and Rohrer invented it in 1981, earning the 1986 Nobel Prize.
难度 专业 · 适合 高中(15-18)
CC BY 4.0 · 已核验 · Verified 2026-11-03
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诺贝尔物理学奖 1986（宾宁与罗雷尔，STM）；《量子力学》隧穿章节
Nobel Prize in Physics 1986 (Binnig & Rohrer, STM); quantum mechanics texts on tunneling
独立核验依据 · Independent verification: 核验依据 1 ISBN 9787040396706（豆瓣书目条目: 量子力学）；本条出处含多部著作，此标识只担保上面点名的这部
#量子隧穿 #扫描隧道显微镜 #势垒
测不准原理说的是仪器不够好吗？
Does the uncertainty principle just reflect imperfect measuring instruments?
不是。它源于波粒二象性：任何粒子既是粒子也是波，位置越确定，对应的动量（波长）就越不确定。海森堡给出严格关系：位置不确定度与动量不确定度的乘积不小于约h/(4π)。这写在量子态本身的性质里，与测量技巧无关。教科书里光子撞偏电子只是帮助理解的比喻，真正的原因是粒子的波动性。
No — it follows from wave-particle duality. Every particle is both particle and wave, and the better you fix its position, the less definite its momentum (wavelength) becomes. Heisenberg's relation sets the product of the two uncertainties no smaller than about h/(4π). This is intrinsic to the quantum state, independent of instrument quality. The textbook image of a photon kicking an electron is only an analogy; the real origin is the wave nature of matter.
难度 专业 · 适合 高中(15-18)
CC BY 4.0 · 已核验 · Verified 2026-10-03 · 2 条独立证据
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《费曼物理学讲义》第三卷（量子行为）
The Feynman Lectures on Physics, Vol. 3 (quantum behavior)
独立核验依据 · Independent verification: 核验依据 2 ISBN 978-0-7382-0298-3 (2006 Pearson 版，原始版为1963-65 Addis
#测不准原理 #海森堡 #波粒二象性
什么是量子叠加态？
What is a quantum superposition?
量子叠加指一个微观系统可以同时处于多个可能状态的线性组合，直到被测量时才随机塌缩到某一确定状态。著名的薛定谔猫思想实验正是用宏观比喻来说明这一点。
Quantum superposition means a system can exist as a combination of several possible states at once, randomly collapsing to one definite state upon measurement. Schrodinger's cat thought experiment uses a macroscopic analogy for this.
难度 专业 · 适合 高中(15-18)
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
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曾谨言,《量子力学 卷I》,科学出版社,2013
Zeng Jinyan, Quantum Mechanics Vol.I, Science Press, 2013
独立核验依据 · Independent verification: 核验依据 2 DOUBAN ISBN 标识 9787030387226（按标识回读: 量子力学 卷1）
#叠加态 #量子 #测量
兰姆位移为什么说明电磁真空并非空无一物？
Why does the Lamb shift demonstrate that the electromagnetic vacuum is far from empty?
狄拉克方程预言氢原子 2S₁/₂ 与 2P₁/₂ 能级严格简并，但兰姆与雷瑟福用微波共振测得二者劈裂约 1058 MHz。量子电动力学把这个位移归因于电子与真空零点涨落的耦合，并包含真空极化与顶点修正的贡献。该实验成为重整化 QED 的关键判据，直接证明真空涨落具有可观测的物理效应。
Dirac's equation predicts exact degeneracy of the hydrogen 2S₁/₂ and 2P₁/₂ levels, yet Lamb and Retherford's microwave resonance found them split by about 1058 MHz. Quantum electrodynamics attributes this shift to the electron coupling to vacuum zero-point fluctuations, including contributions from vacuum polarization and vertex corrections. The experiment served as a decisive test of renormalized QED and proved directly that vacuum fluctuations carry observable physical effects.
难度 专业 · 适合 高中(15-18)
CC BY 4.0 · 已核验 · Verified 2026-11-04
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W. E. Lamb Jr., R. C. Retherford,《Fine Structure of the Hydrogen Atom by a Microwave Method》,Physical Review,1947 (DOI: 10.1103/physrev.72.241)
W. E. Lamb Jr. and R. C. Retherford, 'Fine Structure of the Hydrogen Atom by a Microwave Method', Physical Review, 1947, DOI: 10.1103/physrev.72.241
独立核验依据 · Independent verification: 核验依据 1 Crossref DOI 10.1103/physrev.72.241
#量子电动力学 #兰姆位移
什么是量子语境性？Kochen-Specker 定理怎样排除非语境隐变量模型？
What is quantum contextuality, and how does the Kochen-Specker theorem rule out non-contextual hidden-variable models?
该定理指出，在三维以上希尔伯特空间中，无法给每个投影算符赋一个与测量语境无关的 0 或 1，并要求任意正交基内恰有一个投影取 1；任何此类赋值都必然自相矛盾。于是“测量结果由系统预先决定、与其他共测观测量无关”的非语境隐变量模型被排除，表明量子性质并非预先备好的清单，而是依赖于具体的测量安排。
The theorem shows that in Hilbert spaces of dimension three or higher you cannot assign every projection operator a definite value of 0 or 1, independently of measurement context, such that within any orthogonal basis exactly one projection equals 1; every such assignment contradicts itself. Non-contextual hidden-variable models, in which outcomes are fixed in advance regardless of which other observables are measured jointly, are therefore ruled out, revealing contextuality as an intrinsic feature of quantum systems.
难度 专业 · 适合 高中(15-18)
CC BY 4.0 · 已核验 · Verified 2026-11-03
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S. Kochen 与 E. P. Specker，《量子力学中的隐变量问题》，Journal of Mathematics and Mechanics 第 17 卷（1967）第 59–87 页，DOI: 10.1512/iumj.1968.17.17004
S. Kochen & E. P. Specker, The Problem of Hidden Variables in Quantum Mechanics, Journal of Mathematics and Mechanics 17 (1967) 59–87, DOI: 10.1512/iumj.1968.17.17004
独立核验依据 · Independent verification: 核验依据 1 INSPIRE 标识 10.1512/iumj.1968.17.17004：The Problem of Hid
#量子基础 #语境性 #隐变量
植物叶片吸收光子之后，这份激发能为什么会几乎毫无损失地直达反应中心，而不是沿途以热或荧光的形式散失掉？
After a leaf absorbs a photon, why does the excitation energy almost always arrive at the reaction center intact instead of being lost along the way as heat or fluorescence?
因为天线色素构成一条「下坡」的能量漏斗：叶绿素因蛋白环境不同而吸收能级略有差异，激发态主要经Foerster共振能量转移逐级向下跳迁。供体并不发光，而是振荡偶极子直接驱动受体跃迁，速率随距离六次方锐减且要求光谱重叠；相邻色素仅距一至二纳米，每步只需皮秒，远快于荧光耗散，故能量几乎必然汇入反应中心。
Because the antenna pigments form an energetically downhill funnel: each chlorophyll's absorption level shifts slightly with its protein environment, so excitations hop stepwise downward, mostly via Foerster resonance energy transfer. The donor never emits a photon; its oscillating dipole drives the acceptor transition directly, at a rate falling with the sixth power of separation and requiring spectral overlap. Neighboring pigments sit only 1-2 nm apart, so each hop takes picoseconds, far faster than fluorescence decay, and the descending ladder funnels virtually every excitation into the reaction center.
难度 专业 · 适合 高中(15-18)
CC BY 4.0 · 来源待核验 · Source pending review
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出处备注：此条未指向带版次的可引用著作（通识性内容、机构文件或未展开的英文书名），本库不提供独立书目出处；如需精确引用，需由编辑补全具体篇目与版次。
T. Foerster,Naturwissenschaften,1946；Z. Liu et al.,Nature,2004
T. Foerster, Naturwissenschaften, 1946; Z. Liu et al., Nature, 2004
#光合作用 #共振能量转移 #激子
什么是光电效应？
What is the photoelectric effect?
光电效应指光照射金属表面时把电子打出来的现象，且电子能量只与光的频率有关，与光强无关。爱因斯坦用光量子说解释了它，这成为量子论的重要证据。
The photoelectric effect is the ejection of electrons from a metal by light, where electron energy depends only on light frequency, not intensity. Einstein explained it with light quanta, a key piece of evidence for quantum theory.
难度 进阶 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
曾谨言,《量子力学 卷I》,科学出版社,2013
Zeng Jinyan, Quantum Mechanics Vol.I, Science Press, 2013
独立核验依据 · Independent verification: 核验依据 2 DOUBAN ISBN 标识 9787030387226（按标识回读: 量子力学 卷1）
#光电效应 #光子 #爱因斯坦
泡利不相容原理是什么？
What is the Pauli exclusion principle?
泡利不相容原理指出，两个全同费米子（如电子）不能占据完全相同的量子态。它解释了原子中电子为何分层排布，从而决定了元素周期表和物质稳定性。它是费米子统计的直接结果。
The Pauli exclusion principle states that two identical fermions (such as electrons) cannot occupy exactly the same quantum state. It explains why electrons in atoms occupy shells, thereby determining the periodic table and the stability of matter. It is a direct consequence of fermionic statistics.
难度 进阶 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
曾谨言,《量子力学 卷I》,科学出版社,2013
Zeng Jinyan, Quantum Mechanics Vol.I, Science Press, 2013
独立核验依据 · Independent verification: 核验依据 2 DOUBAN ISBN 标识 9787030387226（按标识回读: 量子力学 卷1）
#泡利不相容 #费米子 #原子
康普顿散射如何验证光子具有动量？
How does Compton scattering verify that photons carry momentum?
康普顿发现X射线被电子散射后波长变长，且偏移量可用光子与电子的弹性碰撞公式精确算出。这说明光子像粒子一样带有动量p=h/λ。它是光粒子性的又一关键证据。
Compton found that X-rays scattered by electrons have a longer wavelength, and the shift matches the formula for an elastic collision between a photon and an electron. This shows photons carry momentum p=h/λ like particles. It is another key proof of light's particle nature.
难度 进阶 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
曾谨言,《量子力学 卷I》,科学出版社,2013
Zeng Jinyan, Quantum Mechanics Vol.I, Science Press, 2013
独立核验依据 · Independent verification: 核验依据 2 DOUBAN ISBN 标识 9787030387226（按标识回读: 量子力学 卷1）
#康普顿散射 #光子动量 #碰撞
光照到金属表面为什么能打出电子？为什么频率太低的光再强也打不出来？
Why does light knock electrons out of metal, and why can't intense low-frequency light do it no matter how bright?
光由一个个光子组成，每个光子携带的能量正比于它的频率。电子要挣脱金属需要获得一份最低能量（逸出功），而且它只能一次性吸收一个光子，所以只有光子能量大于逸出功时才能把电子打出来。频率太低的光子能量不足，光照再强也无济于事；而频率足够高的光哪怕很微弱也能打出电子。爱因斯坦因此提出光量子假说，并荣获1921年诺贝尔物理学奖。
Light is made of photons, each carrying energy proportional to its frequency. An electron needs a minimum energy, the work function, to escape, and it absorbs photons one at a time, so only photons above that energy can eject it. Low-frequency photons can't do the job however intense the beam, while high-frequency light works even when dim. Einstein's photon hypothesis explained this and won him the 1921 Nobel Prize in Physics.
难度 进阶 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-10-03 · 2 条独立证据
来源 · Source
《费曼物理学讲义》第三卷（量子行为）
The Feynman Lectures on Physics, Vol. 3 (quantum behavior)
独立核验依据 · Independent verification: 核验依据 2 ISBN 978-0-7382-0298-3 (2006 Pearson 版，原始版为1963-65 Addis
#光电效应 #光子 #爱因斯坦
爱因斯坦说的鬼魅般的超距作用究竟指什么？
What exactly did Einstein mean by spooky action at a distance?
两个粒子可以形成纠缠态：单个粒子的性质（如自旋方向）事先并不确定，但两者之间存在严格关联。测量其中一个，另一个的性质瞬间被确定，哪怕它们隔了亿万公里。爱因斯坦认为这违背相对论精神，称之为鬼魅般的超距作用。后来的贝尔实验证明这种关联真实存在，无法用预先安排好的隐藏参数解释。但它不违反因果律，也不能用来超光速传递信息。
Two particles can share an entangled state: each one's property, like spin direction, is undetermined beforehand, yet the two are strictly linked. Measuring one instantly fixes the other's, even across astronomical distances. Einstein thought this violated relativity's spirit and called it spooky action at a distance. Bell tests later proved the correlation is real and can't be explained by pre-agreed hidden variables — yet it breaks no causality and can't transmit information faster than light.
难度 进阶 · 适合 初中(12-15)
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
曾谨言,《量子力学 卷I》,科学出版社,2013
Zeng Jinyan, Quantum Mechanics Vol.I, Science Press, 2013
独立核验依据 · Independent verification: 核验依据 2 DOUBAN ISBN 标识 9787030387226（按标识回读: 量子力学 卷1）
#量子纠缠 #贝尔不等式 #量子信息
原子里的电子是怎样排布的？
How are electrons arranged in an atom?
电子分布在原子核外不同的能级和轨道上，离核越近能量越低。泡利不相容原理限制了每个轨道最多容纳两个自旋相反的电子。
Electrons occupy different energy levels and orbitals outside the nucleus, with lower energy closer in. The Pauli exclusion principle limits each orbital to two electrons of opposite spin.
难度 进阶 · 适合 初中(12-15)
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
曾谨言,《量子力学 卷I》,科学出版社,2013
Zeng Jinyan, Quantum Mechanics Vol.I, Science Press, 2013
独立核验依据 · Independent verification: 核验依据 2 DOUBAN ISBN 标识 9787030387226（按标识回读: 量子力学 卷1）
#电子 #原子 #能级
双缝实验为什么被认为是量子力学最诡异的实验？
Why is the double-slit experiment called the strangest in quantum mechanics?
单个电子一个一个发射，长期累积却仍在屏上形成明暗相间的干涉条纹，仿佛每个电子同时走过两条缝并和自己干涉。更奇怪的是一旦在缝旁放探测器「看」它走哪条缝，干涉条纹就消失、只剩两道亮带——观测本身改变了结果。托马斯·杨1801年先做光的版本，后来证明电子等也如此。
Even when electrons are fired one at a time, the accumulated pattern shows interference fringes, as if each electron went through both slits and interfered with itself. Stranger still, placing a detector at the slits to 'see' the path makes the fringes vanish into two bands—observation changes the outcome. Young demonstrated the light version in 1801; later experiments showed electrons do it too.
难度 进阶 · 适合 初中(12-15)
CC BY 4.0 · 已核验 · Verified 2026-10-04
来源 · Source
托马斯·杨 1801 年双缝实验；费曼《物理学讲义》第三卷对双缝的讲解
T. Young (1801) double-slit; Feynman Lectures on Physics, Vol. III, on the double-slit
独立核验依据 · Independent verification: 核验依据 1 ISBN 978-0-7382-0298-3 (2006 Pearson 版，原始版为1963-65 Addis
#双缝实验 #波粒二象性 #量子干涉
什么是德布罗意物质波？
What is the de Broglie matter wave?
德布罗意提出，不仅光，所有物质粒子也都具有波动性，其波长 λ=h/p 与动量成反比。电子衍射实验证实了这一点。它把波粒二象性推广到一切物质，是量子力学的奠基石之一。
De Broglie proposed that not only light but all matter particles have wave nature, with wavelength λ=h/p inversely proportional to momentum. Electron diffraction experiments confirmed it. It extended wave-particle duality to all matter and is a cornerstone of quantum mechanics.
难度 进阶 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
曾谨言,《量子力学 卷I》,科学出版社,2013
Zeng Jinyan, Quantum Mechanics Vol.I, Science Press, 2013
独立核验依据 · Independent verification: 核验依据 2 DOUBAN ISBN 标识 9787030387226（按标识回读: 量子力学 卷1）
#德布罗意 #物质波 #波长
激光为什么能发出如此集中而单色的光？
Why can a laser emit such focused, monochromatic light?
激光靠受激辐射让大量原子步调一致地放出相同相位、相同频率的光子，形成相干光束；谐振腔再筛选出沿轴传播的单一模式。Maiman 于 1960 年用红宝石造出第一台激光器。
A laser uses stimulated emission so many atoms release photons of identical phase and frequency, forming a coherent beam; the cavity selects a single mode traveling along the axis. Maiman built the first ruby laser in 1960.
难度 进阶 · 适合 初中(12-15)
CC BY 4.0 · 已核验 · Verified 2026-10-04
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Svelto《激光原理》；Maiman 1960 年论文
Svelto, Principles of Lasers; Maiman (1960)
独立核验依据 · Independent verification: 核验依据 1 ISBN 9781461576716 (2016)
#激光 #受激辐射 #相干光
测不准原理限制了什么？
What does the uncertainty principle limit?
海森堡测不准原理指出，位置与动量、能量与时间等共轭量无法同时被任意精确地确定。这不是仪器不够好，而是量子本身的属性。它给微观世界设定了根本的认知边界。
Heisenberg's uncertainty principle states that conjugate quantities like position and momentum, or energy and time, cannot both be arbitrarily precise at once. This is not a flaw of instruments but an intrinsic quantum property. It sets a fundamental epistemic boundary on the microscopic world.
难度 进阶 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
曾谨言,《量子力学 卷I》,科学出版社,2013
Zeng Jinyan, Quantum Mechanics Vol.I, Science Press, 2013
独立核验依据 · Independent verification: 核验依据 2 DOUBAN ISBN 标识 9787030387226（按标识回读: 量子力学 卷1）
#测不准 #海森堡 #共轭量
玻色子与费米子有什么根本区别？
What is the fundamental difference between bosons and fermions?
区别在于统计：玻色子服从玻色-爱因斯坦统计，可无限占据同一量子态；费米子服从费米-狄拉克统计，受泡利不相容原理限制。前者是力的传递者（如光子），后者构成物质（如电子）。这与自旋为整数或半整数密切相关。
The difference is in statistics: bosons obey Bose-Einstein statistics and can occupy the same state without limit, while fermions obey Fermi-Dirac statistics and are restricted by the Pauli principle. The former mediate forces (like photons), the latter make up matter (like electrons). This is tied closely to integer versus half-integer spin.
难度 进阶 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
曾谨言,《量子力学 卷I》,科学出版社,2013
Zeng Jinyan, Quantum Mechanics Vol.I, Science Press, 2013
独立核验依据 · Independent verification: 核验依据 2 DOUBAN ISBN 标识 9787030387226（按标识回读: 量子力学 卷1）
#玻色子 #费米子 #统计
量子纠缠真的能超光速传递信息吗？
Can quantum entanglement really transmit information faster than light?
纠缠粒子间的关联是瞬时的，但单独一方的测量结果完全随机，无法用来编码信息。要比较两端结果仍需经典通信，而经典通信受光速限制。因此纠缠不违背相对论，也不能超光速通信。
The correlations between entangled particles are instantaneous, but each side's individual result is completely random and cannot encode a message. Comparing the two ends still needs classical communication, which is limited by light speed. Thus entanglement neither violates relativity nor enables faster-than-light communication.
难度 进阶 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
曾谨言,《量子力学 卷I》,科学出版社,2013
Zeng Jinyan, Quantum Mechanics Vol.I, Science Press, 2013
独立核验依据 · Independent verification: 核验依据 2 DOUBAN ISBN 标识 9787030387226（按标识回读: 量子力学 卷1）
#量子纠缠 #超光速 #信息
阿哈罗诺夫-玻姆效应说明了什么？
What does the Aharonov-Bohm effect show?
该效应表明，即使粒子经过的区域磁场为零，只要周围的磁矢势不为零，电子的相位仍会改变，并在干涉实验中显现。这说明势（而非仅场）具有直接的物理意义。它凸显了规范势的真实地位。
The Aharonov-Bohm effect shows that even where the magnetic field is zero along a particle's path, a nonzero magnetic vector potential around it shifts the electron's phase and shows up in interference. This means potentials, not just fields, have direct physical meaning. It highlights the genuine status of gauge potentials.
难度 进阶 · 适合 初中(12-15)
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
曾谨言,《量子力学 卷I》,科学出版社,2013
Zeng Jinyan, Quantum Mechanics Vol.I, Science Press, 2013
独立核验依据 · Independent verification: 核验依据 2 DOUBAN ISBN 标识 9787030387226（按标识回读: 量子力学 卷1）
#阿哈罗诺夫-玻姆 #矢势 #相位
量子计算机用的“量子比特”和日常比特哪里不同？
How does a quantum bit differ from an ordinary bit?
普通比特非 0 即 1，量子比特可处于 0 和 1 的叠加，还能与别的量子比特纠缠。这让某些计算（如大数分解、搜索）能并行探索许多可能性。
A normal bit is 0 or 1; a qubit can be a superposition of both and can entangle with others. That lets some tasks—factoring, searching—explore many possibilities at once.
难度 进阶 · 适合 初中(12-15)
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
Griffiths & Schroeter,《Introduction to Quantum Mechanics》第3版,Cambridge University Press,2018
D. J. Griffiths and D. F. Schroeter, Introduction to Quantum Mechanics, 3rd ed., Cambridge University Press, 2018
独立核验依据 · Independent verification: 核验依据 2 ARCHIVE 标识 introduction-to-quantum-mechanics_202510：Intr
#量子比特 #叠加 #量子计算
电子双缝实验中观察者起什么作用？
What role does the observer play in the electron double-slit experiment?
在双缝实验中，若探测电子通过哪条缝，干涉条纹就会消失，电子表现得像粒子。关键不在于意识，而在于测量行为干扰了系统、获取了路径信息。这说明量子系统对信息的可获取性极为敏感。
In the double-slit experiment, if you detect which slit each electron uses, the interference pattern vanishes and electrons behave like particles. The key is not consciousness but that the measurement disturbs the system and acquires path information. It shows quantum systems are exquisitely sensitive to information accessibility.
难度 进阶 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
曾谨言,《量子力学 卷I》,科学出版社,2013
Zeng Jinyan, Quantum Mechanics Vol.I, Science Press, 2013
独立核验依据 · Independent verification: 核验依据 2 DOUBAN ISBN 标识 9787030387226（按标识回读: 量子力学 卷1）
#双缝实验 #测量 #干涉
量子退相干如何解释经典世界的涌现？
How does quantum decoherence explain the emergence of the classical world?
退相干指量子系统与环境相互作用，使其叠加相位信息迅速扩散到环境中，使宏观叠加在实际上无法观测。它并不解决测量问题的全部，但解释了为何我们看不到日常物体的叠加。经典性由此在开放系统中自然出现。
Decoherence occurs when a quantum system interacts with its environment, spreading superposition phase information outward so macroscopic superpositions become practically unobservable. It does not fully solve the measurement problem but explains why we do not see everyday objects in superposition. Classicality thus emerges naturally in open systems.
难度 进阶 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
曾谨言,《量子力学 卷I》,科学出版社,2013
Zeng Jinyan, Quantum Mechanics Vol.I, Science Press, 2013
独立核验依据 · Independent verification: 核验依据 2 DOUBAN ISBN 标识 9787030387226（按标识回读: 量子力学 卷1）
#退相干 #经典极限 #环境
什么是量子隧穿？
What is quantum tunneling?
量子隧穿指粒子有一定概率穿过按经典力学无法跨越的势垒。因为粒子具有波动性，波函数在势垒内指数衰减却不为零，于是有非零概率出现在另一侧。它是核聚变的太阳能源机制和隧道二极管的基础。
Quantum tunneling means a particle has a nonzero probability of crossing a barrier that classical mechanics forbids. Because the particle is wavelike, its wavefunction decays exponentially inside the barrier yet remains nonzero, so it can appear on the other side. It underlies the Sun's fusion energy and tunnel diodes.
难度 进阶 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
曾谨言,《量子力学 卷I》,科学出版社,2013
Zeng Jinyan, Quantum Mechanics Vol.I, Science Press, 2013
独立核验依据 · Independent verification: 核验依据 2 DOUBAN ISBN 标识 9787030387226（按标识回读: 量子力学 卷1）
#量子隧穿 #势垒 #波函数
海森堡不确定性原理是说因为我们测不准，还是因为本来就测不准？
Does Heisenberg's uncertainty principle mean we just measure poorly, or that nature is fundamentally uncertain?
它是自然界的根本限制，不是仪器不够好：一个粒子的位置和动量不能同时被任意精确地确定，位置越确定，动量就越不确定（Δx·Δp ≥ ħ/2）。同样，能量和时间也有类似关系。这源于微观粒子兼具波与粒子的本性，是量子力学的核心，而非实验误差。
It is a fundamental limit of nature, not a measurement flaw: a particle's position and momentum cannot both be arbitrarily precise—the more exactly you know one, the less the other (Δx·Δp ≥ ħ/2). Energy and time obey a similar relation. It follows from the wave–particle nature of microscopic objects and is central to quantum mechanics, not experimental error.
难度 进阶 · 适合 初中(12-15)
CC BY 4.0 · 已核验 · Verified 2026-11-03
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W. 海森堡 1927 年论文；《量子力学》（L. D. 朗道与栗弗席兹）相关章节
W. Heisenberg (1927) paper; Landau & Lifshitz, 'Quantum Mechanics', on the uncertainty relation
独立核验依据 · Independent verification: 核验依据 1 ISBN 9787040396706（豆瓣书目条目: 量子力学）；本条出处含多部著作，此标识只担保上面点名的这部
#不确定性原理 #测不准 #量子力学
量子纠缠到底是什么意思，为什么爱因斯坦说它「鬼魅般的超距作用」？
What does quantum entanglement mean, and why did Einstein call it 'spooky action at a distance'?
两个粒子若处于纠缠态，它们的属性（如自旋）就绑在一起：测其中一个立刻知道另一个的结果，无论相距多远。爱因斯坦认为这暗示存在「隐变量」、违背定域性，故称其鬼魅。但阿斯佩1982年及后续实验（违背贝尔不等式）证实纠缠真实存在，且不能用于超光速传递信息。
Entangled particles have bound properties (e.g., spin): measuring one instantly tells you the other's outcome however far apart. Einstein thought this implied hidden variables and violated locality, calling it spooky. Yet Aspect's 1982 experiment and later tests (violating Bell's inequality) confirmed entanglement is real, though it cannot send information faster than light.
难度 进阶 · 适合 小学高段(9-12)
CC BY 4.0 · 已核验 · Verified 2026-11-04
来源 · Source
阿斯佩、达利巴尔、罗歇（Aspect, Dalibard, Roger）,《Experimental Test of Bell's Inequalities Using Time- Varying Analyzers》,Physical Review Letters,1982 (DOI: 10.1103/physrevlett.49.1804)；爱因斯坦-波多尔斯基-罗森 1935 年论文
Aspect, Dalibard and Roger, 'Experimental Test of Bell's Inequalities Using Time- Varying Analyzers', Physical Review Letters, 1982, DOI: 10.1103/physrevlett.49.1804; Einstein–Podolsky–Rosen (1935)
独立核验依据 · Independent verification: 核验依据 1 Crossref DOI 10.1103/physrevlett.49.1804
#量子纠缠 #贝尔不等式 #非定域性
泡利不相容原理限制了什么？
What does the Pauli exclusion principle restrict?
该原理规定同一量子体系中不能有两个全同费米子占据完全相同的量子态。它决定了电子在原子壳层的排布，从而解释元素周期表的结构与物质为何有体积。
The principle forbids two identical fermions from occupying the same quantum state in one system. It dictates how electrons fill atomic shells, explaining the structure of the periodic table and why matter has volume.
难度 进阶 · 适合 高中(15-18)
CC BY 4.0 · 已核验 · Verified 2026-11-03
来源 · Source
泡利 1925 年论文；Shankar《量子力学原理》
Pauli (1925); Shankar, Principles of Quantum Mechanics
独立核验依据 · Independent verification: 核验依据 1 OPENLIBRARY 标识 /works/OL1255103W：The Principles of Quant
#泡利不相容原理 #费米子 #原子壳层
为什么钠灯发出的是黄色光，而不是各种颜色的混合？
Why is sodium-vapor light yellow instead of a blend of all colors?
原子里的电子只能占据特定的能级，并在能级之间跳跃。电子从高能级跃迁到低能级时，多余的能量以光子的形式发出，光子能量恰好等于两个能级的能量差，而光子能量决定了光的颜色。钠原子最强的跃迁对应波长为589纳米的光，所以钠灯呈现特有的黄光。每种元素都有自己的特征谱线，天文学家正是靠它判断恒星的化学成分。
Electrons in an atom occupy only specific energy levels and jump between them. When one drops from a higher level to a lower one, the surplus energy leaves as a photon whose energy equals the level spacing, and that energy fixes the color. Sodium's strongest transition emits light of wavelength 589 nanometers, which is why sodium lamps glow characteristic yellow. Every element has its own fingerprint spectral lines, which is how astronomers identify the elements in stars.
难度 进阶 · 适合 初中(12-15)
CC BY 4.0 · 已核验 · Verified 2026-10-03 · 2 条独立证据
来源 · Source
《费曼物理学讲义》第三卷（能级）
The Feynman Lectures on Physics, Vol. 3 (energy levels)
独立核验依据 · Independent verification: 核验依据 2 ISBN 978-0-7382-0298-3 (2006 Pearson 版，原始版为1963-65 Addis
#能级 #光谱线 #原子跃迁
粒子“穿墙”是怎么回事，真能发生吗？
How can a particle tunnel through a wall—does it really happen?
在量子力学里，遇到比自身能量还高的势垒，粒子仍有一定概率出现在墙的另一侧，这叫隧穿。它是真实效应：太阳核聚变、闪存和扫描隧道显微镜都靠它。
In quantum mechanics a particle hitting a barrier higher than its energy still has some probability of appearing on the other side—tunneling. It is real: the Sun's fusion, flash memory, and scanning tunneling microscopes all rely on it.
难度 进阶 · 适合 高中(15-18)
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
Griffiths & Schroeter,《Introduction to Quantum Mechanics》第3版,Cambridge University Press,2018
D. J. Griffiths and D. F. Schroeter, Introduction to Quantum Mechanics, 3rd ed., Cambridge University Press, 2018
独立核验依据 · Independent verification: 核验依据 2 ARCHIVE 标识 introduction-to-quantum-mechanics_202510：Intr
#量子隧穿 #势垒 #概率
二极管为什么只允许电流朝一个方向通过？
Why does a diode allow current to flow in only one direction?
二极管由P型半导体和N型半导体拼接而成：P区富含带正电的空穴，N区富含自由电子。加正向电压时，电子和空穴被推向交界处并相互复合，形成持续的电流；加反向电压时，交界处会形成一个几乎没有载流子的耗尽区，把电流挡住。正是这个单向导通的性质，让二极管成为整流、检波等电路的基石。
A diode joins P-type and N-type semiconductors — the P side rich in positively charged holes, the N side in free electrons. Forward bias pushes electrons and holes toward the junction, where they recombine and sustain a current; reverse bias widens a carrier-free depletion region at the junction that blocks current. This one-way behavior makes diodes the foundation of rectification and signal detection.
难度 进阶 · 适合 初中(12-15)
CC BY 4.0 · 已核验 · Verified 2026-10-03
来源 · Source
S. M. Sze 与 Kwok K. Ng 著《Physics of Semiconductor Devices》（半导体器件物理）
S. M. Sze & Kwok K. Ng, Physics of Semiconductor Devices
独立核验依据 · Independent verification: 核验依据 1 ISBN 9780470068328
#二极管 #PN结 #整流
什么是量子芝诺效应？
What is the quantum Zeno effect?
量子芝诺效应指，如果对一个未稳定的量子系统进行频繁测量，系统会因每次测量将其重置而无法演化，仿佛被看住而停滞。它源于测量使波函数坍缩、打断演化的机制。已在离子阱等实验中观测到。
The quantum Zeno effect means that frequent measurements of an unstable quantum system keep resetting it through collapse, preventing evolution, as if being watched froze it. It arises because measurement collapses the wavefunction and interrupts evolution. It has been observed in ion-trap experiments.
难度 进阶 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
曾谨言,《量子力学 卷I》,科学出版社,2013
Zeng Jinyan, Quantum Mechanics Vol.I, Science Press, 2013
独立核验依据 · Independent verification: 核验依据 2 DOUBAN ISBN 标识 9787030387226（按标识回读: 量子力学 卷1）
#量子芝诺 #测量 #波函数坍缩
泡利不相容原理怎样决定了原子和电子的排布？
How does the Pauli exclusion principle determine how atoms and electrons are arranged?
它规定两个全同费米子（如电子）不能占据完全相同的量子态。于是原子里的电子必须一层层、按不同轨道和自旋排开，形成壳层结构，这才有了元素周期表的规律和化学性质的差异。若没有这条原理，所有电子会挤进最低能态，原子将塌缩成毫无结构的点，世界也就不是现在的样子。
It forbids two identical fermions (such as electrons) from occupying the same quantum state. So electrons in an atom must fill shells and subshells with distinct orbitals and spins, creating the periodic table's structure and the variety of chemistry. Without it, all electrons would pile into the lowest state and atoms would collapse into structureless points—the world would be unrecognizable.
难度 进阶 · 适合 小学高段(9-12)
CC BY 4.0 · 已核验 · Verified 2026-11-03
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W. 泡利 1925 年提出不相容原理；沃尔夫冈·泡利《泡利物理学讲义》原子物理卷
W. Pauli (1925) exclusion principle; Pauli, 'Pauli Lectures on Physics', atomic physics volume
独立核验依据 · Independent verification: 核验依据 1 OPENLIBRARY 标识 /works/OL6862865W：Lectures on Physics (Pa
#泡利不相容原理 #费米子 #电子排布
波粒二象性到底指什么？
What exactly does wave-particle duality mean?
微观粒子（如电子、光子）既表现出粒子性又表现出波动性：单个事件像局域的“点”，大量事件的分布却遵循波动干涉规律。Davisson-Germer 于 1927 年用电子衍射直接证实了电子的波动性。
Microscopic particles such as electrons and photons show both particle and wave behavior: each individual event looks like a localized hit, yet the statistical pattern obeys wave interference. Davisson and Germer confirmed electron waves by diffraction in 1927.
难度 进阶 · 适合 初中(12-15)
CC BY 4.0 · 已核验 · Verified 2026-10-04
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Feynman《物理学讲义》第三卷；Davisson-Germer 1927 年论文
Feynman, The Feynman Lectures on Physics (Vol. III); Davisson & Germer (1927)
独立核验依据 · Independent verification: 核验依据 1 ISBN 978-0-7382-0298-3 (2006 Pearson 版，原始版为1963-65 Addis
#波粒二象性 #电子衍射 #物质波
氢原子受激发后为什么会只发出某些特定波长的光谱线，而不是任意颜色？
Why does an excited hydrogen atom emit only certain specific wavelengths, not any color?
玻尔模型与后来量子力学都表明，氢原子的电子只能处于分立的能级。电子从高能级跳回低能级时，释放的光子能量等于两级之差，对应固定的波长，于是谱线分立。这正是氢原子特征发射谱（如巴尔末系）的来源。
Both the Bohr model and later quantum mechanics show that a hydrogen electron can occupy only discrete energy levels. When it drops from a higher to a lower level, the emitted photon's energy equals the gap, fixing the wavelength, so the spectrum is line-based. This is the origin of hydrogen's characteristic series such as the Balmer lines.
难度 进阶 · 适合 初中(12-15)
CC BY 4.0 · 已核验 · Verified 2026-10-03
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D. J. Griffiths,《Introduction to Quantum Mechanics》(第2版),第4章(氢原子)
D. J. Griffiths, 'Introduction to Quantum Mechanics' (2nd ed.), Ch.4 (The hydrogen atom)
#氢原子光谱 #能级 #玻尔模型
什么是量子？
What is a quantum?
量子是物理量的最小不可分割单位，比如能量只能以一份一份的离散形式交换。这意味着微观世界不是连续变化的，而是跳跃式的。
A quantum is the smallest indivisible unit of a physical quantity, such as energy exchanged only in discrete packets. It means the microscopic world changes in jumps rather than continuously.
难度 进阶 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
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曾谨言,《量子力学 卷I》,科学出版社,2013
Zeng Jinyan, Quantum Mechanics Vol.I, Science Press, 2013
独立核验依据 · Independent verification: 核验依据 2 DOUBAN ISBN 标识 9787030387226（按标识回读: 量子力学 卷1）
#量子 #离散 #不连续
光电效应如何证明光的粒子性？
How does the photoelectric effect prove the particle nature of light?
爱因斯坦解释：光由能量为hν的光子组成，只有当单个光子能量足以打出电子时才会产生光电流，且电子动能随频率而非光强增大。这无法用经典波动理论解释。它为量子论和光子概念奠定了基础。
Einstein explained that light consists of photons with energy hν, and a photocurrent appears only when a single photon has enough energy to eject an electron; the electron's kinetic energy grows with frequency, not intensity. Classical wave theory cannot explain this. It established the quantum theory and the photon concept.
难度 进阶 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
曾谨言,《量子力学 卷I》,科学出版社,2013
Zeng Jinyan, Quantum Mechanics Vol.I, Science Press, 2013
独立核验依据 · Independent verification: 核验依据 2 DOUBAN ISBN 标识 9787030387226（按标识回读: 量子力学 卷1）
#光电效应 #光子 #爱因斯坦
同样是固体，为什么金属能导电、玻璃却不导电？
Why do metals conduct electricity while glass does not, even though both are solids?
固体中大量原子的能级扩展成一条条能带，电子在能带中的填充情况决定了导电性。金属的最高能带只被部分填满，电子很容易获得能量参与导电；绝缘体的能带要么填满要么全空，中间隔着很宽的禁带，电子几乎无法跃过去。半导体的禁带宽度很小，所以光照、温度或掺杂都能显著改变它的导电能力。
In a solid, the levels of countless atoms spread into energy bands, and how electrons fill them decides conduction. In metals the highest band is partially filled, so electrons easily gain energy and carry current; in insulators the bands are full or empty, separated by a wide gap that electrons cannot cross. Semiconductors have a narrow gap, which is why light, temperature or doping can dramatically change their conductivity.
难度 进阶 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-10-03 · 2 条独立证据
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《费曼物理学讲义》第三卷（半导体）
The Feynman Lectures on Physics, Vol. 3 (semiconductors)
独立核验依据 · Independent verification: 核验依据 2 ISBN 978-0-7382-0298-3 (2006 Pearson 版，原始版为1963-65 Addis
#能带 #导体 #绝缘体
电子怎么也会有“波长”？
How can an electron have a wavelength?
德布罗意提出所有物质都有波动性，波长 λ=h/p 由动量决定。电子波长极短，但用晶体当作“光栅”仍能看到衍射，证实了物质波。
de Broglie proposed that all matter has wave nature, with λ=h/p set by momentum. An electron's wavelength is tiny, yet crystals act as a grating and reveal its diffraction, confirming matter waves.
难度 进阶 · 适合 小学高段(9-12)
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
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Griffiths & Schroeter,《Introduction to Quantum Mechanics》第3版,Cambridge University Press,2018
D. J. Griffiths and D. F. Schroeter, Introduction to Quantum Mechanics, 3rd ed., Cambridge University Press, 2018
独立核验依据 · Independent verification: 核验依据 2 ARCHIVE 标识 introduction-to-quantum-mechanics_202510：Intr
#物质波 #德布罗意 #衍射
元素周期表和量子力学有什么关系？
What is the link between the periodic table and quantum mechanics?
元素的性质随原子序数周期性变化，其根源在于电子在不同能级和轨道上的排布规律。量子力学用四个量子数精确描述了电子状态，从而解释了周期表的结构。
Element properties vary periodically with atomic number because of how electrons fill energy levels and orbitals. Quantum mechanics uses four quantum numbers to describe electron states, explaining the periodic table's structure.
难度 进阶 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
曾谨言,《量子力学 卷I》,科学出版社,2013
Zeng Jinyan, Quantum Mechanics Vol.I, Science Press, 2013
独立核验依据 · Independent verification: 核验依据 2 DOUBAN ISBN 标识 9787030387226（按标识回读: 量子力学 卷1）
#元素周期表 #电子排布 #量子数
真空真的是空无一物吗?兰姆位移和卡西米尔效应各自如何证明真空涨落会产生可测量的物理后果?
Is the vacuum truly empty, and how do the Lamb shift and the Casimir effect each demonstrate that vacuum fluctuations have measurable physical consequences?
在量子电动力学中,真空是所有场的基态,仍然保有零点涨落。氢原子的2S与2P能级因束缚电子与真空涨落及虚光子的相互作用而发生微小劈裂,这就是兰姆位移。两块中性导体板会改变板间真空模式的密度,从而感受到可测量的相互吸引,这就是卡西米尔效应。
In quantum electrodynamics the vacuum is the ground state of all fields and still retains zero-point fluctuations. The hydrogen 2S level splits slightly from 2P because the bound electron interacts with vacuum fluctuations and virtual photons, which is the Lamb shift. Two neutral conducting plates alter the density of vacuum modes between them and feel a measurable attraction, which is the Casimir effect.
难度 进阶 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-11-04
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W. E. Lamb 与 R. C. Retherford, Phys. Rev. 72, 241 (1947); H. B. G. Casimir, Proc. K. Ned. Akad. Wet. 51, 793 (1948)
W. E. Lamb & R. C. Retherford, Phys. Rev. 72, 241 (1947); H. B. G. Casimir, Proc. K. Ned. Akad. Wet. 51, 793 (1948)
独立核验依据 · Independent verification: 核验依据 1 Crossref DOI 10.1103/physrev.72.241
#兰姆位移 #卡西米尔效应
在单电子双缝实验中，电子一颗一颗地发出，为什么屏幕上仍会慢慢累积出干涉条纹？
In the single-electron double-slit experiment, electrons are sent one at a time — why do interference fringes gradually build up on the screen anyway?
每个电子落到屏幕哪一点是随机的，像一颗粒子；但它的运动由波函数支配，来自两条缝的振幅会叠加或抵消，使落点密集处形成亮纹、稀疏处形成暗纹。大量单次事件累积后便显现出清晰的干涉条纹。这说明干涉并非发生在不同电子之间，而是每个电子自身同时经历两条路径的结果，正是波粒二象性的直接体现。
Where any single electron lands on the screen is random, like a particle, yet its motion is governed by a wavefunction: the amplitudes from the two slits add or cancel, making arrivals dense where they reinforce and sparse where they cancel out. Accumulating many such events reveals clear interference fringes. The interference therefore happens within each individual electron, which travels through both paths simultaneously — a direct display of wave-particle duality.
难度 进阶 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-11-02
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A. Tonomura 等， Demonstration of single-electron buildup of an interference pattern, American Journal of Physics 57, 117-120 (1989), DOI: 10.1119/1.16104
A. Tonomura et al., Demonstration of single-electron buildup of an interference pattern, American Journal of Physics 57, 117-120 (1989), DOI: 10.1119/1.16104
独立核验依据 · Independent verification: 核验依据 1 CROSSREF 标识 10.1119/1.16104：Demonstration of single-elec
#量子基础 #波粒二象性 #双缝实验
薛定谔的猫想说明什么？
What does Schrödinger's cat illustrate?
这个思想实验把量子叠加放大到宏观：猫在开箱前同时处于活着和死了的叠加。薛定谔用它讽刺把微观叠加直接套用到宏观世界是荒谬的。它促使人们思考量子到经典的边界在哪里。
This thought experiment scales quantum superposition to the macroscopic: before opening the box the cat is in a superposition of alive and dead. Schrödinger used it to mock the absurdity of applying microscopic superposition directly to the macroscopic world. It pushes us to ask where the quantum-to-classical boundary lies.
难度 入门 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
曾谨言,《量子力学 卷I》,科学出版社,2013
Zeng Jinyan, Quantum Mechanics Vol.I, Science Press, 2013
独立核验依据 · Independent verification: 核验依据 2 DOUBAN ISBN 标识 9787030387226（按标识回读: 量子力学 卷1）
#薛定谔的猫 #叠加 #宏观
什么是量子比特？
What is a qubit?
量子比特是量子计算的基本单元，与只能取0或1的经典比特不同，它能处于|0⟩和|1⟩的任意叠加。多个量子比特还能通过纠缠产生经典无法高效模拟的关联。它是量子计算优势的根源。
A qubit is the basic unit of quantum computing; unlike a classical bit that is 0 or 1, it can be in any superposition of |0⟩ and |1⟩. Multiple qubits can become entangled, producing correlations no classical system simulates efficiently. This is the source of quantum computing's advantage.
难度 入门 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
曾谨言,《量子力学 卷I》,科学出版社,2013
Zeng Jinyan, Quantum Mechanics Vol.I, Science Press, 2013
独立核验依据 · Independent verification: 核验依据 2 DOUBAN ISBN 标识 9787030387226（按标识回读: 量子力学 卷1）
#量子比特 #叠加 #量子计算
光的本质是什么——波还是粒子？
What is the nature of light—wave or particle?
光既不是经典意义上的纯波，也不是纯粒子，而是具有波粒二象性的量子客体（光子）。在传播时表现出干涉、衍射等波动特征，在与物质相互作用时表现为离散的能量包。现代物理用量子电动力学统一描述它。
Light is neither a purely classical wave nor a purely classical particle; it is a quantum object (the photon) with wave-particle duality. It shows interference and diffraction while propagating, yet appears as discrete energy packets when interacting with matter. Modern physics describes it uniformly through quantum electrodynamics.
难度 入门 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
曾谨言,《量子力学 卷I》,科学出版社,2013
Zeng Jinyan, Quantum Mechanics Vol.I, Science Press, 2013
独立核验依据 · Independent verification: 核验依据 2 DOUBAN ISBN 标识 9787030387226（按标识回读: 量子力学 卷1）
#光子 #波粒二象性 #量子电动力学