量子力学简明教程

I Basic Concepts and Main Applicatio

1 The Discovery of Quantum Theory

1.1 Blackbody Radiation and Planck‘s Hypothesis of Energy Quanta

1.2 Photoelectric Effect and Ei tein’s Hypothesis of Light Quanta

1.3 The Atomic Spectra and Bohr‘s Model of Atoms

2 Wavefunction and Schr6dinger Equation

2.1 The de Broglie Hypothesis and Davisson-Germer Experiment

2.2 Schrodinger Equation

2.3 Stationary Solutio

2.4 General Properties of Motion in One Dime ion

2.5 Bound States in Potential Well

2.5.1 Square Well of Infinite Depth

2.5.2 Square Well of Finite Depth

2.6 The Harmonic Oscillator

2.7 Tunnelling Effect

3 Operato and Heisenberg Uncertainty Relation

3.1 Observables and Operato

3.2 Hermitian Operato and Their Properties

3.3 Some Example Operato

3.3.1 Momentum Operato and Their Eigenfunctio

3.3.2 Angular Momentum Operato and Their Eigenfunctio

3.3.3 Coordinate Representation and Momentum Representation

3.4 Evaluation of the Expectation Values

3.5 The Heisenberg Uncertainty Relation

3.5.1 Commutation Relatio and Their Implicatio

3.5.2 Uncertainty Relation and the Minimum Uncertainty State

3.6 The Time Evolution of Expectation Values

4 Motion in a Centrally Symmetric Field

4.1 Three Dime ional Harmonic Oscillato

4.2 The Feature of Motion in a Centrally Symmetric Field

4.3 Spherical Waves and Plane Waves

4.4 Motion in a Coulomb Field

4.5 Hydrogen-like Energy Levels

4.6 Hydrogen Atom and Hydrogen-like Io

5 States and Heisenberg Equation

5.1 Matrix Representation of Operato

5.2 States and Their Representatio

5.3 The Heisenberg Equation

5.4 Algebraic Approach for Harmonic Oscillator

5.5 Algebraic Approach for Angular Momentum

II Developing Skills

6 Bound-State Perturbation and Correctio to Energy Levels

6.1 Nondegenerate Perturbation TheOry

6.2 Degenerate Perturbation Theory

6.3 Stark Effect

7 Time-dependent Perturbation and Quantum Tra itio

7.1 Perturbation Depending on Time

7.2 Tra ition Probability

7.2.1 Periodic Perturbation of Single Frequency

7.2.2 Tra ition to Continuous Spectrum

7.3 Induced Absorption and Emission

7.4 Ei tein’s Semi-phenomenological Theory for Spontaneous Emission

8 Scattering Theory for Elastic Collisio

8.1 Scattering Amplitude and Cross Section

8.2 Born Approximation

8.2.1 The Simplest Approach

8.2.2 Lippmann-Schwinger Equation

8.2.3 Scattering by Screened Coulomb Potential

8.3 Partial-Wave Approach

8.3.1 Phase Shifts and Scattering Amplitudes for Centrally Symmetric Potentials

8.3.2 Neutron-Proton Scattering

8.3.3 The Center-of-Mass Frame and the Lab Frame

9 Motion in a Magnetic Field

9.1 Schrodinger Equation for a Charged Particle in Electromagnetic Fields

9.2 Electro in a Uniform Magnetic Field

9.3 Atoms in Magnetic Field and Zeeman Effect

9.4 Electron Spin

9.5 Spin-Orbit Coupling and the Fine Structure of Atomic Spectra

9.5.1 On Spin-Orbit Coupling

9.5.2 On the Fine Structure of Atomic Spectra

10 Identical Particles and Pauli Exclusive Principle

10.1 Permutation Symmetry and the Indistinguishability of Identical Particles

10.2 Noninteracting Systems，Pauli Exclusive Principle

10.2.1 Two-particle Systems

10.2.2 N-particle Systems

10.3 Interacting Systems

10.3.1 Helium Atom，Hund‘s Rule

A Matrix and Vector Space

B δ-function

C Confluent Hypergeometric Function

D Orbitals for d-Electro

E Lab Frame and Center-of-mass Frame

F On an Integral

G Time Reve al and Krame Degeneracy

This is based on the authorsfollowing two principles： （i） if a textbook were so perfectly arranged that leaves nothing to be desired, it would make the readers feel that the scientific discovery is so mystical that they lose passion of creativity.