ADVANCED QUANTUM MECHANICS UPON THEOREMS

ADVANCED QUANTUM MECHANICS UPON THEOREMS

Library of Congress Cataloging-in-Publication Data

Contents

Preface

Chapter 1 Quantum Mechanics upon Theorems

1.1 Introduction

1.2 Bases of Quantum Mechanics

1.3 Stationary States of One Dimension System

1.4 General Formalism

1.5 Hellmann-Feynman Theorems

1.6 Identical Particles

1.7 Time-Dependent Tr nsition Theory

1.8 Dissociated States

1.9 Big Theorem of Energy

1.10 Big Theorem of Wavepacket

Chapter 2 Second Quantization Method

2.1 Introduction

2.2 Bosons

2.3 Fermions

2.4 One- and Two-Body Operators of Bosons

2.4.1 One-Body Operators of Bosons

2.4.2 Two-Body Operators of Bosons

2.5 One- and Two-Body Operators of Fermions

2.6 Field Operators

Chapter 3 Electron and Phonon in Condensed Matter

3.1 Introduction

3.2 Free Fermi Gas

3.3 Interacting Electron Gas

3.4 Phonon

3.5 Electron-Phonon Interaction

3.6 Exercises and Solutions

Chapter 4 Scattering Theory

4.1 Introduction

4.2 Scattering Matrix

4.3 Scattering Theory

4.4 Exercises and Solutions

Chapter 5 Quantum Relaxation

5.1 Introduction

5.2 Linewidth-Lifetime Product

5.3 Non- ebye Relaxation in Condensed Matters

5.4 General Study for Survival Probability

5.5 Exercises and Solutions

Chapter 6 Applications in Energy Sources

6.1 Cold Fusion

6.2 Internal Conversion

Chapter 7 Microscopic Superconductivity

7.1 Introduction

7.2 BCS Pairing Theory

7.3 Microscopic Superconductivity

7.4 Spontaneous Symmetry Breaking

7.5 Exercises and Solutions

Chapter 8 Relativistic Quantum Mechanics

8.1 Introduction

8.2 Related Recalls from Chapter 1

8.3 Klein-Gorden Equation

8.4 Dirac Equation

8.5 Free Particle Solution of Dirac Equation

8.6 Symmetries of Dirac Objects

8.7 Composition of Dirac Spinor Wavepacket

Chapter 9 Bases of Quantum Field Theory

9.1 Introduction

9.2 Theorems and Steps

9.3 Quantization of Schr¨odinger Equation

9.4 Quantization of Klein-Gorden Equation

9.5 Quantization of Dirac Equation

9.6 Quantization of Maxwell Field Equation

9.7 Future of Quantum Field Theory

Chapter 10 Fractional Quantum Mechanics upon Theorems

10.1 Introduction

10.2 Fractional Derivative

10.3 Composition Theorem of Fractional Wavepacket

10.4 Fractional Schr¨odinger Equation

10.5 Fractional Uncertainty Relation

Appendix A Special Theory of Relativity

A.1 Physics

A.2 Notations of Special Theory of Relativity

A.3 Forms of Gamma Matrices

Appendix B Classical Field Theory

B.1 Recall on Multiparticles

B.2 Lagrangian and Hamiltonian Formulations of Classical Field

Appendix C  Function

C.1 Definition of  Function

C.2 Properties of  Function

C.3 One Dimensional  Functions

C.4 Three Dimensional  Functions

C.5 Longitudinal and Transverse  Functions

Bibliography

Index