简明量子力学

Preface

1 Introduction

1.1 Introduction

1.2 Schrodinger's Equation

1.3 Eigenfunctions

1.4 Measurement

1.5 Representations

1.5.1 Schrodinger Representation

1.5.2 Heisenberg Representation

1.6 Noncommuting Operators

2 One Dimension

2.1 Square Well

2.2 Linear Potentials

2.3 Harmonic Osallator

2.4 Raising and Lowering Operators

2.5 Exponential Potential

2.5.1 Boun,d State

2.5.2 Contin,uum State

2.6 Delta-Function Potential

2.7 Number of Solutions

2.8 Normalization

2.8.1 Boun,d States

2.8.2 Box Normalization

2.8.3 Delta-Function Normalization

2.8.4 The Limit of Infinite Volume

2.9 Wave Packets

3 Approximate Methods

3.1 WKBJ

3.2 Bound States by WKBJ

3.2.1 Harmonic Oscillator

3.2.2 Morse Potential

3.2.3 Symmetric Ramp

3.2.4 Discontinuous Potentials

3.3 Electron Tunneling

3.4 Variational Theory

3.4.1 Half-Space Potential

3.4.2 Harmonic Oscillator in One Dimension

4 Spin and Angular Momentum

4.1 Operators, Eigenvalues, and Eigenfunctic

4.1.1 Commutation Relations

4.1.2 Raising and Lowering Operators

4.1.3 Eigenfun,aions an,d Eigenvalues

4.2 Representations

4.3 Rigid Rotations

4.4 The Addition ofAngular Momentum

5 Two and Three Dimensions

5.1 Plane Waves in Three Dimensions

5.2 Plane Waves in Two Dimensions

5.3 Central Potentials

5.3.1 Central Potentials in 3D

5.3.2 Central Potential in 2D

5.4 Coulomb Potentials

5.4.1 Bound States

5.4.2 Confluent Hypergeometric Functions

5.4.3 Hydrogen Eigenfunaions

5.4.4 Continuum States

5.5 WKBJ

5.5.1 Three Dimensions

5.5.2 3D Hvdrogen Atom

5.5.3 Two Dimensions

……

6 Matrix Methods and Perturbation Theory

7 Time-Dependent Perturbations

8 Electromagnetic Radiation

9 Many-Particle Systems

10 Scattering Theory

11 Relativistic Quantum Mechanics

Index

This manuscript is a textbook for a graduate course in quantum mechanics.I have taught this course 15-20 times and gradually developed these notes. Orginally，I used as a text Quantum Mechanics by A.S.Davydov.When that fine book went out of print，I wrote these notes following a similar syllabus.It contains much new material not found in older texts.
　　The beginning chapters follow a traditional syllabus.Topics include solving Schrodingers equation in one，two，and three dimensions.Approximate techniques are introduced such as（1）variational，（2）WKBJ，and（3）perturbation theory.Many examples are taken from the quantum mechanics of atoms and small molecules.Solid-state ex-amples include exchange energy，Landau levels，and the quantum Hall effect.later chapters discuss scattering theory and relativistic quantum mechanics.The chapter on optical properties includes both linear and nonlinear optical phenomena. Each chapter concludes with numerous homework problems.
　　Preliminary versions of these lectures have been handed to several generations of graduate students.Their feedback has been invaluable in honing the material.