This book is intended for use as a textbook for a graduate course
in Advanced Quantum Mechanics, and as a reference book for
workers in the field.
Before the subject is presented, a brief but seIf-contained review
on the foundation of Quantum Mechanics is given. A large part of
this book is devoted to select applications of quantum mechanics,
such as scattering theory, second quantization, superconductive
theory, superfluidity, phase of wave function, path integral and
relativistic quantum mechanics. The selection is guided by the
interest of topic to physicists, its value as an illustration of
calculating techniques, and our personal taste.
To read the book, the reader need basic knowledge of quantum
mechanics, some intuitive feeling for electrodynamics and special
relativity, and a good mathematical knowledge.
CONTENTS
PREFACE
Chapter 1 Foundation of Quantum Mechanics
1. 1 State Vector, Wave Function and Superposition of States
1. 2 Schr0dinger Equation and Its Solutions
1. 3 Operators
1. 4 Approximation Methods
1. 5 WKB Approximation
1. 6 Density Matrix
Chapter 2 Scattering Theory
2. 1 General Description of the Scattering Theory
2. 2 The Partial Wave Method
2. 3 Examples of the Partial Wave Method
2. 4 Green Function Method and Bom Approximation
2. 5 Center-of mass Coordinate and the Laboratorv Coordinf
2. 6 T Matrix
2. 7 Lippman-Schwinger Equation
2. 8 Dyson Equation
2. 9 Scattering Matrix(S Matrix)
2. 10 Scattering in the Complex Potential
2. 11 General Theory of the Inelastic Scattering
2. 12 Approximation of the Distortion Wave
Chapter 3 Many Body ProbIem
3. 1 Second Quantization
3. 2 Hartree-Fock Mean Field Approximation
3. 3 Thomas-Fermi Method
3. 4 Superconductive Theory
3. 5 Superfluidity Theory
Chapter 4 Path lntegraI
4. 1 Classical Action and the Amplitude in Quantum Mechanics
4. 2 Path Integral
4. 3 Gauss Integration
4. 4 Path Integral and the Schrodinger Equation
4. 5 The Canonical Form of the Path Integral
Chapter 5 Relativistic Quantum Mechanics
5. 1 Klein-Gordon Equation
5. 2 Dirac Equation
5. 3 Solutions of the Free Field Dirac Equation
5. 4 Dirac Equation in the Electromagnetic Field
5. 5 Covariant Form of the Dirac Equation
5. 6 Dirac Equation in the Central Force Field
5. 7 Solution of the Dirac Equation in the Coulomb Field
5. 8 Klein Paradox
5. 9 MIT Bag Model
5. 10 Chiral symmetry
Chapter 6 Phase of Wave Function
6. 1 Aharanov-Bohm Effect
6. 2 Aharanov-Casher Effect
6. 3 Magnetic Flux of Superconductive Ring
6. 4 Monopole
6. 5 Berry Phase
6. 6 Non-integrable Phase Factor
6. 7 Vacuum Energy and Casimir Effect
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