📚 E.2 Quantum Physics: Photons, Matter Waves and Atomic Spectra | E.2 量子物理：光子、物质波与原子光谱
Quantum physics revolutionised our understanding of the microscopic world, introducing concepts such as quantisation of energy, wave-particle duality, and the inherent uncertainty in measurements. In IB Physics topic E.2, we explore how phenomena like the photoelectric effect, atomic spectra, and electron diffraction led to the development of quantum theory, challenging classical physics.
量子物理彻底改变了我们对微观世界的认识，引入了能量量子化、波粒二象性以及测量中固有的不确定性等概念。在 IB 物理 E.2 主题中，我们探索光电效应、原子光谱和电子衍射等现象如何推动量子理论的发展，并挑战了经典物理学。
1. Introduction to Quantum Physics | 量子物理导论
Classical physics, including Newtonian mechanics and Maxwell's electromagnetism, successfully describes macroscopic phenomena but fails at the atomic scale. Quantum physics emerged in the early 20th century to explain experiments that could not be accounted for by classical theories, such as blackbody radiation, the photoelectric effect, and the discrete line spectra of atoms. Key ideas include the quantisation of energy, the particle-like behaviour of light (photons), and the wave-like behaviour of matter.
经典物理学，包括牛顿力学和麦克斯韦电磁学，成功描述了宏观现象，但在原子尺度上却失效了。量子物理于 20 世纪初出现，用于解释经典理论无法说明的实验，例如黑体辐射、光电效应和原子的分立线状光谱。关键思想包括能量的量子化、光的粒子性（光子）和物质的波动性。
2. Planck's Quantum Hypothesis | 普朗克量子假说
lackbody could only take on discrete values, E = n h f, where n is an integer, h is Planck's constant (6.63 × 10-34 J s), and f is the frequency. This resolved the ultraviolet catastrophe predicted by the classical Rayleigh–Jeans law. Although Planck initially considered quantisation a mathematical trick, it laid the foundation for quantum theory.
1900 年，马克斯·普朗克提出黑体中电磁振荡器的能量只能取分立值 E = n h f，其中 n 为整数，h 为普朗克常数（6.63 × 10-34 J·s），f 为频率。这解决了经典瑞利–金斯定律所预言的紫外灾难。虽然普朗克最初将量子化视为数学技巧，但它为量子理论奠定了基础。
E = n h f, n = 0, 1, 2, …
3. The Photon Model of Light | 光的光子模型
Building on Planck' is the wavelength. This photon model explained the photoelectric effect, in which electrons are emitted from a metal surface when light of sufficiently high frequency shines on it, regardless of intensity.
基于普朗克的思想，阿尔伯特·爱因斯坦于 1905 年提出光本身由分立的能量量子组成，后来称为光子。每个光子携带能量 E = h f 和动量 p = E/c = h / λ，其中 λ 是波长。这个光子模型解释了光电效应，即当频率足够高的光照射到金属表面时，无论光强如何，都会有电子发射出来。
E = h f, p = h / λ
4. The Photoelectric Effect Experiment | 光电效应实验
The photoelectric effect experiment consists of illuminating a metal cathode in a vacuum tube and measuring the resulting current. Key observations: (1) Electrons are only emitted if the incident light frequency exceeds a threshold frequency f0, specific to the metal. (2) The maximum kinetic energy of emitted electrons increases linearly with frequency and is independent of intensity. (3) Increasing intensity increases the number of emitted electrons (photocurrent) but does not affect their maximum kinetic energy. These findings contradict classical wave theory, which predicts that kinetic energy should depend on intensity and that any frequency should eventually eject electrons if the light is intense enough.
光电效应实验包括照射真空管中的金属阴极，并测量产生的电流。关键观察结果：（1）只有当入射光频率超过金属特定的阈值频率 f0 时，才会发射电子。（2）发射电子的最大动能随频率线性增加，与光强无关。（3）增加光强会增加发射电子数目（光电流），但不影响其最大动能。这些发现与经典波动理论相矛盾，经典理论预测动能应依赖于光强，并且只要光强足够大任何频率最终都应能打出电子。
5. Einstein's Photoelectric Equation | 爱因斯坦光电方程
Einstein's photoelectric equation is Kmax = h f – Φ, where Kmax is the maximum kinetic energy of the emitted electron, h f is the photon energy, and Φ is the work function of the metal (the minimum energy needed to eject an electron). If h f < Φ, no electrons are emitted. In an experimental setup, a stopping potential Vs can be applied to reduce the photocurrent to zero; then Kmax = e Vs. A graph of Kmax vs f yields a straight line with slope h and intercept on the frequency axis equal to the threshold frequency f0 = Φ/h, providing a method to measure Planck's constant.
爱因斯坦光电方程为 Kmax = h f – Φ，其中 Kmax 是发射电子的最大动能，h f 是光子能量，Φ 是金属的逸出功（打出电子所需的最小能量）。若 h f < Φ，则没有电子发射。在实验中，可施加遏止电压 Vs 使光电流降为零，此时 Kmax = e Vs。Kmax 与 f 的关系图为一直线，斜率为 h，频率轴截距为阈值频率 f0 = Φ/h，这提供了一种测量普朗克常数的方法。
Kmax = h f – Φ, Kmax = e Vs
6. Wave-Particle Duality | 波粒二象性
Wave-particle duality is the concept that both light and matter exhibit both wave-like and particle-like properties. Light, traditionally considered a wave, displays particle behaviour in the photoelectric effect, where it interacts as discrete quanta. Conversely, electrons, historically thought of as particles, show wave-like interference and diffraction patterns. This duality is a fundamental aspect of quantum mechanics, encapsulated by de Broglie's hypothesis that every moving particle has an associated wavelength.
波粒二象性是指光与物质都表现出波动性和粒子性。传统上被视为波的光，在光电效应中显示出粒子行为，以分立的量子相互作用。与之相对，历史上被认为是粒子的电子，却表现出波的干涉和衍射图样。这种二象性是量子力学的一个基本特征，由德布罗意假说所概括，即每个运动粒子都有一个相应的波长。
7. de Broglie Wavelength | 德布罗意波长
n electron accelerated through a potential difference V, its kinetic energy is e V = ½ m v2, so momentum p = √2 m e V, and the de Broglie wavelength λ = h / √2 m e V. Using typical values, an electron accelerated through 100 V has a wavelength of about 0.12 nm, which is comparable to atomic spacing and enables diffraction by crystal lattices.
1924 年，路易·德布罗意提出，任何具有动量 p 的运动粒子都具有一个相应的波长 λ = h / p。对于有质量的粒子，除非粒子非常轻（如电子），否则这个波长极小。对于经电势差 V 加速的电子，其动能为 e V = ½ m v2，因此动量 p = √2 m e V，德布罗意波长为 λ = h / √2 m e V。代入典型值，经 100 V 加速的电子波长约为 0.12 nm，与原子间距相当，从而能够被晶格衍射。
λ = h / p, λ = h / √2 m e V
8. Electron Diffraction and Matter Waves | 电子衍射与物质波
The wave nature of electrons was confirmed by
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