Quantum Mechanics: Zhou Shan

13.7.3 Feynman’s Hypothesis 13.7.4 Optical Analogy *13.8 The Classical Limit 13.8.1 Path Integral Formulation 13.8.2 Canonical Formulation Exercises Chapter 14: Systems of Identical Particles 14.1 Description of the System 14.1.1 Characteristics of Identical Particles 14.1.2 Two-Electron System 14.1.3 Principle of Indistinguishability 14.2 Two-Particle Systems 14.2.1 State Space 14.2.2 Particles with Spin 14.2.3 Spin State Space *14.2.4 Measurement of Spin *14.2.5 Exchange Force 14.3 Three-Particle Systems 14.3.1 Permutation Operators 14.3.2 State Vectors 14.4 N-Particle Systems 14.4.1 State Vectors 14.4.2 Number of Microstates 14.4.3 Linear Operators *14.5 Fock Space 14.5.1 Construction of the Space 14.5.2 Creation and Annihilation Operators ★ Fundamental Postulates of Quantum Mechanics ★ Exercises Chapter 15: Stationary Perturbation Theory 15.1 Two-State Systems 15.1.1 Non-Degenerate Unperturbed Energy Levels 15.1.2 Degenerate Unperturbed Energy Levels 15.2 Foundations of Perturbation Theory 15.2.1 Perturbation Series 15.2.2 Corrections at Each Order 15.3 Non-Degenerate Case 15.3.1 First-Order Correction 15.3.2 Second-Order Correction *15.3.3 Third-Order Correction *15.3.4 Formal Notation *15.3.5 Generalization of Results 15.4 Degenerate Case 15.4.1 First-Order Energy Correction *15.4.2 Second-Order Energy Correction 15.5 Preliminary Applications of Perturbation Theory 15.5.1 Harmonic Oscillator in an Electric Field 15.5.2 Stark Effect *15.6 Fine Structure of Energy Levels 15.6.1 Perturbation Term 15.6.2 Relativistic Effects 15.6.3 Spin–Orbit Coupling 15.6.4 Darwin Term *15.7 Zeeman Effect 15.7.1 Hamiltonian Operator 15.7.2 Strong-Field Zeeman Effect 15.7.3 Weak-Field Zeeman Effect 15.7.4 Intermediate-Field Zeeman Effect Exercises Chapter 16: Quantum Transitions 16.1 Time Evolution of State Vectors 16.2 Perturbative Approximation 16.3 Periodic Perturbations 16.3.1 Transition Probability and Transition Rate 16.3.2 Characteristics of Transitions 16.3.3 Cases with Complex Energy Spectra 16.3.4 Constant Perturbation 16.4 Harmonic Oscillator in an Electric Field *16.5 Emission and Absorption of Light 16.5.1 Perturbed Hamiltonian 16.5.2 Linearly Polarized Light Incidence 16.5.3 Natural (Unpolarized) Light Incidence 16.5.4 Selection Rules 16.5.5 Spontaneous Emission Exercises Chapter 17: Non-Perturbative Approximations 17.1 Variational Method 17.1.1 Concept of the Variational Method 17.1.2 Preliminary Applications 17.1.3 Ground State of the Helium Atom 17.2 Adiabatic Approximation 17.2.1 Adiabatic Theorem 17.2.2 Berry Phase 17.3 WKB Approximation 17.3.1 WKB Wavefunction 17.3.2 Simple Applications 17.3.3 Slowly Varying Potential Well Exercises Chapter 18: Scattering 18.1 Description of Scattering 18.1.1 Scattering Cross Section 18.1.2 Scattering Amplitude *18.2 Green’s Function Method

The Mysterious 'New Continent' of Quantum Physics

02 What Is the Photoelectric Effect? So, what exactly is the photoelectric effect? In short, it concerns how light generates electricity (see Figure 1). If blue light shines on a conductive metal such as copper, electrons—tiny negatively charged particles orbiting atomic nuclei vastly larger than themselves, while the nuclei carry positive charge—may sometimes be ejected from the metal. The movement of these electrons produces an electric current that can be measured and utilized. The color of light matters: if red light is used instead of blue light, no electrons are ejected and no current flows. This phenomenon has been known since experiments conducted by the German physicist Heinrich Hertz in 1887. A major puzzle regarding the photoelectric effect was that light was then thought to behave purely as a wave (like ocean waves). According to wave theory, continuously increasing the intensity of red light—i.e., sending more red light waves—should eventually make the wave amplitude large enough to eject electrons and generate current. So why does red light fail to do this, whereas even extremely faint blue light succeeds? Einstein solved this puzzle in 1905. He proposed that light should not be viewed as a wave, but rather as discrete ‘packets’ of energy—massless entities. Blue light carries significantly more energy per packet than red light, which explains why only blue light triggers the photoelectric effect. One can imagine these energy packets as tiny billiard balls: if one strikes an electron with sufficient energy, the electron may be knocked out of the metal. This seemingly bizarre idea successfully explained the photoelectric effect; these tiny light ‘packets’ were named photons—the Greek word for light. This astonishing new concept was not the end of the story; in fact, it marked only the beginning. In the years that followed, numerous strange and astonishing phenomena were discovered—a completely new world governed by entirely new laws! Newton’s orderly, predictable universe—akin to a vast machine composed of many small parts—had been replaced by a surprising, uncharted new continent! Physicists did not discard Newton’s laws; they remain valid for explaining and predicting many phenomena, such as the Moon orbiting Earth or a stone falling to the ground. Yet, in the microscopic realm, a vast and entirely new continent had been discovered. 03 The Enigma of Quantum Jumps You may already know that all matter consists of countless atoms. Atoms resemble miniature solar systems—so small that even the most powerful microscopes cannot resolve them. Within these miniature solar systems, electrons orbit the nucleus (the ‘sun’) much like planets orbit the Sun. Physicists discovered that when electrons gain or lose energy, they can jump from orbits closer to the nucleus to those farther away—and vice versa. The wonder of the quantum world lies in the fact that these tiny ‘planets’ (electrons) leap instantaneously from one orbit to another in a single quantum jump. They always reside precisely on a specific orbit—either close to the nucleus or farther away—but never midway between orbits, nor at one-third or one-quarter of the distance. For example, an electron near an atom’s nucleus may absorb a photon and gain energy; then, in the next instant, it finds itself in a more distant orbit.

Morning Bid: Quantum Leap

Jun 3, 2026

Oil prices rose over 2% to $98 per barrel amid Gulf hostilities, while tech stocks hit record highs driven by AI themes. Microsoft announced a quantum computing breakthrough targeting commercial viability within three years.

reuters

2026-06-03

Morning Bid: Quantum Leap

Morning Bid: Quantum Leap

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