📚 IB Physics: Quantum Physics | IB物理：量子物理
Quantum physics is the branch of physics that describes the behaviour of matter and energy at atomic and subatomic scales. At this scale, the concepts of continuous energy and definite trajectories that work in classical physics break down.
量子物理是描述物质与能量在原子和亚原子尺度上行为的物理学分支。在这个尺度上，经典物理中能量连续与轨道确定的概念不再适用。
For IB Physics students, quantum physics connects experimental observations such as the photoelectric effect, atomic spectra, and electron diffraction to a more accurate model of nature. It also introduces the probability-based view of the world that underpins modern technology.
对于IB物理学生而言，量子物理将光电效应、原子光谱、电子衍射等实验观测与更精确的自然模型联系起来，并引入了以概率为基础的现代世界观。
1. Why Quantum Physics? | 为什么学习量子物理？
Classical physics assumes that light is a continuous wave and that an electron moves along a definite path. These assumptions fail when experiments are performed with very small objects or very high frequencies.
经典物理假定光是一种连续的波，电子沿确定路径运动。然而，当我们对非常小的物体或极高频率进行实验时，这些假设就会失效。
Quantum theory was developed to explain observations that classical wave theory could not explain. These observations include the photoelectric effect, line spectra, and the diffraction of electrons.
量子理论正是为了解释经典波动理论无法说明的现象而发展起来的，这些现象包括光电效应、线状光谱和电子衍射。
In the IB syllabus, quantum physics is not just a set of formulas. It is a way of interpreting experiments and understanding that matter can behave as a wave and radiation can behave as a particle.
在IB课程大纲中，量子物理不仅仅是一套公式，更是一种解释实验——理解物质可以表现出波动性、辐射可以表现出粒子性——的方式。
2. The Photoelectric Effect | 光电效应
The photoelectric effect is the emission of electrons from a metal surface when light shines on it. The emitted electrons are called photoelectrons.
光电效应是指当光照射金属表面时，电子从金属表面逸出的现象，这些被发射出的电子称为光电子。
In the classical wave model, the energy carried by light depends only on its intensity. According to that model, any light of sufficiently high intensity should eventually eject electrons from any metal.
在经典波动模型中，光携带的能量只取决于光的强度。按照这一模型，任何足够强的光最终都应该能使金属中的电子逸出。
Experiments showed that this prediction is wrong. The key observations were surprising:
然而实验证明这一预言是错误的，其中关键观察结果令人意外：
- No electrons are emitted if the light frequency is below a certain threshold, no matter how intense the light is.
如果光频率低于某一截止频率，无论光多强，都不会有电子逸出。 - The maximum kinetic energy of photoelectrons increases with frequency, but not with intensity.
光电子的最大动能随频率增大而增大，却与光强度无关。 - Electron emission is essentially instantaneous, even at very low light intensity.
即使光强非常低，电子的逸出也几乎是瞬间发生的。
3. Einstein’s Photon Model | 爱因斯坦的光子模型
In 1905, Einstein explained the photoelectric effect by proposing that light is made of discrete packets of energy called photons. Each photon carries energy proportional to its frequency.
1905年，爱因斯坦提出光由称为光子的离散能量包组成，从而解释了光电效应。每个光子携带的能量与频率成正比。
E = hf
Here, E is the photon energy, f is the frequency of light, and h is Planck’s constant. The value of h is 6.63 × 10⁻³⁴ J s.
其中，E是光子能量，f是光的频率，h是普朗克常量，其值为6.63 × 10⁻³⁴ J·s。
In this model, one photon interacts with one electron. If a photon has enough energy, it can transfer all of its energy to a single electron. Increasing intensity means more photons, not more energy per photon.
在这一模型中，一个光子与一个电子相互作用。如果光子能量足够大，它就能把全部能量传递给一个电子。增加光强意味着光子数量增多，而不是每个光子的能量变大。
4. Work Function and Threshold Frequency | 逸出功与截止频率
Not all of the photon energy becomes kinetic energy. Some of it must be used to remove the electron from the metal surface. This minimum energy is called the work function, Φ.
并非所有光子能量都会转化为动能，其中一部分必须用于将电子从金属表面拉出。这个最小能量称为逸出功，符号为Φ。
The maximum kinetic energy of a photoelectron is therefore given by the photoelectric equation:
因此，光电子的最大动能由光电效应方程给出：
Eₖ(max) = hf − Φ
If the photon energy is less than the work function, no photoelectron can be emitted. The threshold frequency f₀ is the minimum frequency that causes emission:
如果光子能量小于逸出功，则不会有光电子逸出。截止频率f₀是能够引起电子发射的最小频率：
Φ = hf₀
Above the threshold frequency, any extra photon energy appears as kinetic energy of the emitted electron.
当频率高于截止频率时，光子多出的能量表现为逸出电子的动能。
5. Stopping Potential and Kinetic Energy | 遏止电压与动能
In an experiment, the maximum kinetic energy of photoelectrons can be measured using a stopping potential Vₛ. This is the reverse voltage needed to stop all photoelectrons from reaching the collector.
在实验中，可以用遏止电压Vₛ来测量光电子的最大动能。遏止电压是阻止所有光电子到达收集极所需的反向电压。
The electric potential energy gained by an electron in the stopping potential equals the maximum kinetic energy of the photoelectrons:
电子在遏止电压下获得的电势能等于光电子的最大动能：
eVₛ = Eₖ(max)
Here, e is the elementary charge, 1.60 × 10⁻¹⁹ C. Therefore, the stopping potential is directly related to the photon frequency.
其中，e是元电荷，大小为1.60 × 10⁻¹⁹ C。因此遏止电压与光子频率有直接关系。
If Vₛ is plotted against frequency f, the graph is a straight line. Its slope is h/e and its intercept on the frequency axis is f₀. This graph provides a practical way to estimate Planck’s constant.
如果用Vₛ对频率f作图，得到一条直线，其斜率为h/e，与频率轴的交点为f₀。该图像为估算普朗克常量提供了实用方法。
6. Matter Waves: de Broglie Hypothesis | 物质波：德布罗意假说
If light waves can behave like particles, Louis de Broglie asked whether particles such as electrons could behave like waves. In 1924, he proposed that every moving particle has an associated wavelength.
既然光波可以表现得像粒子，路易·德布罗意便思考：电子等粒子是否也能表现得像波。1924年，他提出每个运动的粒子都伴随一个波长。
The de Broglie wavelength is given by:
德布罗意波长由下式给出：
λ = h/p = h/(mv)
Here, p is the momentum of the particle, m is its mass, and v is its velocity. The wavelength is significant only for particles with very small mass.
其中，p是粒子的动量，m是质量，v是速度。只有质量极小的粒子，其物质波波长才会显著。
Electron diffraction experiments confirmed this idea. A beam of electrons can be diffracted by the regular spacing of atoms in a crystal, producing interference patterns just like light waves.
电子衍射实验证实了这一设想。电子束经过晶体中原子周期排列的间隙时会发生衍射，产生类似光波的干涉图样。
7. Wave–Particle Duality | 波粒二象性
Wave–particle duality is the principle that both radiation and matter exhibit both wave-like and particle-like properties, depending on the experiment used to observe them.
波粒二象性是指辐射和物质都具有波的性质与粒子的性质，具体表现出哪一种性质，取决于我们使用何种实验来观察它们。
Light shows particle behaviour in the photoelectric effect and Compton scattering. Light shows wave behaviour in interference and diffraction experiments.
光在光电效应和康普顿散射中表现出粒子性，而在干涉和衍射实验中表现出波动性。
Electrons show particle behaviour when they leave distinct spots on a detector. They show wave behaviour when they produce interference patterns in double-slit or diffraction experiments.
电子在探测器上留下清晰斑点时表现出粒子性，而在双缝或衍射实验中形成干涉图样时则表现出波动性。
It is important to avoid saying that an electron is both a wave and a particle at the same time. The correct idea is that quantum objects are described by a wavefunction, and this wavefunction determines the probability of detecting a particle in a particular place.
重要的一点是：不能说电子同时既是波又是粒子。正确的理解是，量子客体由波函数描述，这个波函数决定了在某个位置探测到粒子的概率。
8. The Uncertainty Principle | 不确定性原理
Werner Heisenberg showed that certain pairs of physical properties cannot both be known with unlimited precision. The most familiar pair is position and momentum.
维尔纳·海森堡指出，某些成对的物理量不可能同时被无限精确地知道。最熟悉的例子是位置和动量。
Δx Δp ≥ h/4π
Here, Δx is the uncertainty in position and Δp is the uncertainty in momentum. This uncertainty is not caused by imperfect measuring instruments; it is a fundamental property of nature.
其中Δx是位置不确定性，Δp是动量不确定性。这种不确定性并非由测量仪器不精确造成，而是自然本身的基本属性。
A similar relationship exists between energy and time:
能量与时间之间也存在类似关系：
ΔE Δt ≥ h/4π
This means that a very short-lived state can have a large uncertainty in energy. This is why excited states in atoms have naturally broad energy widths.
这意味着寿命极短的状态其能量不确定性很大。这也是原子中激发态具有天然能量宽度的原因。
9. Wavefunction and Probability | 波函数与概率
In quantum mechanics, the state of a particle is described by a mathematical object called the wavefunction, usually written as ψ. The wavefunction itself is not measurable directly.
在量子力学中，粒子的状态由称为波函数的数学对象描述，通常记为ψ。波函数本身不能直接被测量。
The probability of finding a particle in a small region is proportional to |ψ|². This quantity is called the probability density.
在一个小区域内找到粒子的概率正比于|ψ|²，这个量称为概率密度。
Where |ψ|² is large, the particle is more likely to be found. Where |ψ|² is zero, the particle will never be found. This is very different from saying that the particle follows a definite path.
在|ψ|²较大的地方，粒子更可能被找到；在|ψ|²为零的地方，粒子永远不会被找到。这与说粒子沿确定路径运动有很大不同。
For IB Physics, the key idea is that quantum physics is probabilistic. The wavefunction contains all the information about the probability of different measurement outcomes.
对于IB物理来说，关键概念是量子物理是概率性的。波函数包含不同测量结果出现概率的全部信息。
10. Energy Levels and Atomic Spectra | 能级与原子光谱
In isolated atoms, electrons can only occupy certain discrete energy levels. Electrons cannot exist with energies between these allowed levels.
在孤立原子中，电子只能占据某些分立能级。电子不能处于这些允许能级之间的能量状态。
When an electron moves from a higher energy level E₂ to a lower energy level E₁, the atom emits a photon. The photon energy equals the difference between the two levels:
当电子从高能级E₂跃迁到低能级E₁时，原子会发射一个光子。光子能量等于两个能级之差：
hf = E₂ − E₁
Using c = fλ, the wavelength of the emitted photon can also be written as:
利用c = fλ，发射光子的波长也可以写成：
hc/λ = E₂ − E₁
Since energy levels are discrete, the emitted wavelengths form a line spectrum. Absorption spectra are produced when electrons absorb photons and jump to higher energy levels.
由于能级是分立的，发射波长形成线状光谱。当电子吸收光子并跃迁到较高能级时，则会产生吸收光谱。
The Balmer series, for example, corresponds to transitions ending at the n = 2 energy level of hydrogen. These lines are in the visible region.
例如，巴耳末系对应氢原子中跃迁到n = 2能级的谱线，这些谱线位于可见光区域。
11. Quantum Tunnelling | 量子隧穿
Quantum tunnelling is a phenomenon in which a particle passes through a potential energy barrier even though its energy is lower than the barrier height. In classical physics, this is impossible.
量子隧穿是指粒子即使能量低于势垒高度，仍然能够穿过势垒的现象。在经典物理中，这是不可能的。
Because the wavefunction does not fall suddenly to zero inside a barrier, there is a small probability that the particle will appear on the other side.
由于波函数在势垒内部不会突然降为零，因此粒子有较小概率出现在势垒的另一侧。
This probability decreases rapidly as the barrier becomes wider or higher. Even so, tunnelling is not a rare event in nature; it is essential for alpha decay, nuclear fusion in stars, and the operation of scanning tunnelling microscopes.
这个概率会随着势垒变宽或变高而迅速减小。然而，隧穿在自然界中并不罕见；它在α衰变、恒星核聚变以及扫描隧道显微镜的工作中都至关重要。
12. Exam Tips for IB Quantum Physics | 考试提示
In IB Physics exams, photoelectric effect questions often require you to state an observation and then explain it with the photon model. Learn the observations listed above and link each one to the idea of photon energy or intensity.
在IB物理考试中，光电效应题目通常要求你陈述一个观察结果，并用光子模型加以解释。最好牢记上文列举的观察结果，并将每一项与光子能量或光子强度联系起来。
- Use the photoelectric equation with consistent units. If energies are given in eV, keep them in eV or convert to joules using 1 eV = 1.60 × 10⁻¹⁹ J.
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