E-Book, Englisch, 168 Seiten, Web PDF
McWeeny Quantum Mechanics
1. Auflage 2013
ISBN: 978-1-4831-8690-0
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark
Principles and Formalism
E-Book, Englisch, 168 Seiten, Web PDF
ISBN: 978-1-4831-8690-0
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark
Quantum Mechanics: Principles and Formalism gives importance to the exposition of the fundamental bases of quantum mechanics. This text first discusses the physical basis of quantum theory. This book then provides some simple solutions of Schrödinger's equation, eigenvalue equations, and general formulation of quantum mechanics. The general theory of representations is also tackled. In discussing this topic, this text specifically looks into the harmonic oscillator, Dirac notation, time-evolution, Schrödinger equation in momentum space, and transformation theory. This publication will be invaluable to students and experts interested in quantum mechanics, especially in the principles of this field of study.
Autoren/Hrsg.
Weitere Infos & Material
1;Front Cover
;1
2;Quantum Mechanics: Principles and Formalism;4
3;Copyright Page
;5
4;Table of Contents
;6
5;PREFACE;8
6;INTRODUCTION;12
7;Chapter 1. Physical Basis of Quantum Theory;14
7.1;1.1. Particles and waves;14
7.2;1.2. The Schrödinger equation for a particle;22
7.3;1.3. Probability density and probability current;26
7.4;1.4. The classical limit for motion of a wave packet;31
8;Chapter 2. Some Simple Solutions of Schrödinger's Equation;34
8.1;2.1. The particle in a container;34
8.2;2.2. The harmonic oscillator;40
8.3;2.3. The hydrogen atom. Atomic units;43
8.4;2.4. The free particle;47
8.5;2.5. One-dimensional step potential with a finite potential height;50
9;Chapter 3. Mathematical Digression;54
9.1;3.1. Preliminaries. Operators and eigenvalue equations;54
9.2;3.2. Eigenfunction expansions;60
9.3;3.3. Generalization to many variables;64
9.4;3.4. Linear vector spaces. Basic ideas;67
9.5;3.5. Matrix representation of operators;72
9.6;3.6. Change of representation;77
9.7;3.7. Hermitian operators and eigenvalue equations in vector space;80
9.8;3.8. Composition of vector spaces. Product space;84
10;Chapter 4. General Formulation of Quantum Mechanics;86
10.1;4.1. The postulates;86
10.2;4.2. The state vector and its time development;87
10.3;4.3. The expectation value postulate;88
10.4;4.4. Significance of the eigenvalue equation;93
10.5;4.5. The uncertainty principle;95
10.6;4.6. Time-development and the energy-time uncertainty principle;97
10.7;4.7. The completeness of eigenfunction sets;99
10.8;4.8. Properties of the operators;105
10.9;4.9. Electron spin;107
11;Chapter 5. General Theory of Representations;117
11.1;5.1. Dirac notation. Discrete case;117
11.2;5.2. An example. The harmonic oscillator;120
11.3;5.3. Dirac notation. Continuous case;122
11.4;5.4. Transformation theory. The momentum representation;127
11.5;5.5. The Schrödinger equation in momentum space;129
11.6;5.6. Time-evolution. The Heisenberg representation;131
11.7;5.7. Representation of incompletely specified states;135
12;Appendix 1. The Schrödinger Equation in Generalized Coordinates;144
13;Appendix 2. Separation of Partial Differential Equations;148
14;Appendix 3. Series Solution of Second-order Differential Equations;152
15;Appendix 4. Projection Operators and Normal Forms;160
16;Index;164
