Preface to the first edition

Century Review of Quantum Physics

Chapter 65438 +0 Wave Function and Schrodinger Equation

Statistical interpretation of 1. 1 wave function

1. 1. 1 volatility of physical particles

Wave-particle duality analysis of 1. 1.2

1. 1.3 probability wave, wave function of multi-particle system

1. 1.4 momentum distribution probability

1. 1.5 uncertainty relation

1. 1.6 average value of mechanical quantities and introduction operator

1. 1.7 Requirements of statistical sampling for wave functions

1.2 Schrodinger equation

1.2. 1 Introduction to Schrodinger Equation

Discussion on 1.2.2 Schrodinger equation

1.2.3 energy eigenequation

1.2.4 steady state and unsteady state

Schrodinger equation of 1.2.5 multi-particle system

The superposition principle of 1.3 quantum states

1.3. 1 quantum state and its representation

Principle, measurement and wave function collapse of 1.3.2 quantum state superposition

Exercise 1

Chapter 2 Particles in One-dimensional Potential Field

2. General properties of particle energy eigenstates in1one-dimensional potential field

2.2 square potential

2.2. 1 infinite square potential well-discrete spectrum

2.2.2 Symmetrical square potential well with finite depth

2.2.3 Bound States and Discrete Spectra

2.2.4 Reflection and transmission of a square barrier

2.2.5 Reflection, transmission and * * * vibration expressed by square potential.

2.3 δ potential

2.3. 1 δ potential penetration

2.3.2 Bound States in δ Potential Well

2.3.3 The relationship between δ potential and square potential, and the jump condition of WeChat service of wave function.

2.4 One-dimensional harmonic oscillator

Exercise 2

Chapter III Mechanical quantities are expressed by operators

3. 1 operator operation rules

3.2 Eigenvalues and Eigenfunctions of Self-adjoint Operators

3.3 *** Homoeigenfunctions

3.3. Strict proof of1uncertainty relation

3.3.2 * * isomorphism and spherical harmonic function of (L2, LZ)

3.4 "Normalization" of continuous spectral characteristic function

3.4. 1 The continuous spectrum eigenfunction cannot be normalized.

δ function

Box standardization

3.4.4 Completion of mechanical quantities

Exercise 3

Chapter IV Evolution and Symmetry of Mechanical Quantities with Time

4. 1 Evolution of mechanical quantities with time

4. 1. 1 conserved quantity

4. 1.2 Relationship between Degeneracy of Energy Level and Conservation Quantity

4.2 Wave Packet Motion, Ellen feaster Theorem

*4.3 Schrodinger image and Heisenberg image

4.4 Relationship between Conservation Quantity and Symmetry

4.5 Exchange Symmetry between identical particles System and Wave Function

4.5. Commutative Symmetry of1identical particles System

4.5.2 The system consists of two identical particles.

4.5.3 System consisting of n identical fermion molecules

4.5.4 A system consisting of n identical Bose subunits

Exercise 4

The fifth chapter center force field

5. 1 General Properties of Particle Motion in Central Force Field

5. 1. 1 conservation of angular momentum and radial equation

5. 1.2 Asymptotic Behavior of Radial Wave Function in r→O Neighborhood

5. 1.3 Two-body problem is transformed into monomer problem.

5.2 Infinite Spherical Square Well

5.3 Three-dimensional isotropic harmonic oscillator

5.4 Hydrogen atom

Exercise 5

Chapter VI Particle Motion in Electromagnetic Field

6. 1 Motion of charged particles in electromagnetic field, two kinds of momentum

6.2 Normal Zeeman Effect

6.3 Landau level

Exercise 6

Chapter VII Matrix Form and Representation Transformation of Quantum Mechanics

* 7. Different representations of1quantum state, unitary transformation

*7.2 Matrix representation of mechanical quantities (operator)

*7.3 Matrix form of quantum mechanics

7.3. 1 Schrodinger equation

average value

characteristic equation

*7.4 Dirac symbol

7.4. 1 right vector (ket) and left vector (bra)

standardized product

7.4.3 Representation of State Vector in Concrete Representation

7.4.4 Representation of Operators in Concrete Representation

Schrodinger equation

Representation transformation

Exercise 7

Chapter VIII Rotation

8. 1 electron spin states and spin operators

8. 1. 1 Description of electron spin states

8. 1.2 electron spin operator, Pauli matrix

8.2 Eigenstate of Total Angular Momentum

8.3 Double-line structure and abnormal Zeeman effect of alkali metal atomic spectrum

8.3. Double-line structure of1alkali metal atomic spectrum

8.3.2 Abnormal Zeeman Effect

8.4 spin singlet and triplet, spin entangled state

Exercise 8

Chapter 9 Algebraic solution of eigenvalue problem of mechanical quantities

9. Schrodinger factorization of1harmonic oscillator

9.2 eigenvalue and eigenstate of angular momentum

9.3 Coupling of two angular momentum, Clebsch-Gordan coefficient

Exercise 9

10 chapter perturbation theory

Perturbation theory of 10. 1 bound state

10. 1. 1 nondegenerate perturbation theory

10. 1.2 degenerate perturbation theory

Perturbation theory of 10.2 scattering state

10.2. 1 description of scattering state

10.2.2 Lipman-Schweiner equation

10.2.3 born approximation

10.2.4 Scattering of the same particle

Exercise 10

Chapter 1 1 Quantum Transition

1 1. 1 evolution of quantum state with time

Systems with Hamiltonian of11.1.1without time.

Perturbation theory of quantum transition in 1 1. 1.2 Hamiltonian time-dependent system

1 1. 1.3 the relationship between quantum transition theory and steady-state perturbation theory

1 1.2 explosive disturbance and adiabatic disturbance

1 1.2. 1 sudden disturbance

1 1.2.2 quantum adiabatic approximation and its establishment conditions

1 1.3 periodic disturbance, constant disturbance in finite time.

1 1.4 energy-time uncertainty relation

1 1.5 Semiclassical theory of light absorption and radiation

1 1.5. 1 light absorption and stimulated radiation

1 1.5.2 Einstein's spontaneous emission theory

Exercise 1 1

Chapter 12 Other Approximation Methods

12. 1 Fermi gas model

12.2 variational method

12.2. 1 energy eigenequation and variational principle

12.2.2 ritz variational method

12.2.3 Hartley method

Molecular structure of 12.3

Born-Oppenheimer approximation

12.3.2 hydrogen molecular ion H2+ and hydrogen molecular H2

Rotation and vibration of 12.3.3 diatomic molecules

Exercise 12

Mathematical appendix

A 1 wave packet

Fourier analysis of A 1. 1 wave packet

Motion and diffusion, phase velocity and group velocity of A 1.2 wave packet

A2 δ function

A2. 1 δ function definition

Some Simple Properties of A2.2 δ Function

A3 Hermite polynomial

A4 legendre polynomials sum spherical harmonic function

A4. 1 legendre polynomials

A4.2 Relevant legendre polynomials

A4.3 spherical harmonic function

A4.4 Several useful extensions

A5 confluence hypergeometric function

A6 Bessel function

A6. 1 Bessel function

A6.2 spherical Bessel function

A7 natural unit

Brief table of common physical constants

Reference book of quantum mechanics