Quantum Mechanics

A unique introductory text on quantum mechanics, from basic principles to historical perspective.
* Includes description of the historical developments that led to the discovery of QM, often left out of other textbooks.
* Emphasizes basic concepts that were essential in this discovery, placing them in context and making them more understandable to students.
* Written in an easy-to-understand style and assuming no prior knowledge of the topic, this book provides a solid foundation for future study of quantum chemistry.
* Includes problem sets for student use.

Preface xi

1 The Discovery of Quantum Mechanics 1

I Introduction 1

II Planck and Quantization 3

III Bohr and the Hydrogen Atom 7

IV Matrix Mechanics 11

V The Uncertainty Relations 13

VI Wave Mechanics 14

VII The Final Touches of Quantum Mechanics 20

VIII Concluding Remarks 22

2 The Mathematics of Quantum Mechanics 23

I Introduction 23

II Differential Equations 24

III Kummer’s Function 25

IV Matrices 27

V Permutations 30

VI Determinants 31

VII Properties of Determinants 32

VIII Linear Equations and Eigenvalues 35

IX Problems 37

3 Classical Mechanics 39

I Introduction 39

II Vectors and Vector Fields 40

III Hamiltonian Mechanics 43

IV The Classical Harmonic Oscillator 44

V Angular Momentum 45

VI Polar Coordinates 49

VII Problems 51

4 Wave Mechanics of a Free Particle 52

I Introduction 52

II The Mathematics of Plane Waves 53

III The Schrödinger Equation of a Free Particle 54

IV The Interpretation of the Wave Function 56

V Wave Packets 58

VI Concluding Remarks 62

VII Problems 63

5 The Schrödinger Equation 64

I Introduction 64

II Operators 66

III The Particle in a Box 68

IV Concluding Remarks 71

V Problems 72

6 Applications 73

I Introduction 73

II A Particle in a Finite Box 74

III Tunneling 78

IV The Harmonic Oscillator 81

V Problems 87

7 Angular Momentum 88

I Introduction 88

II Commuting Operators 89

III Commutation Relations of the Angular Momentum 90

IV The Rigid Rotor 91

V Eigenfunctions of the Angular Momentum 93

VI Concluding Remarks 96

VII Problems 96

8 The Hydrogen Atom 98

I Introduction 98

II Solving the Schrödinger Equation 99

III Deriving the Energy Eigenvalues 101

IV The Behavior of the Eigenfunctions 103

V Problems 106

9 Approximate Methods 108

I Introduction 108

II The Variational Principle 109

III Applications of the Variational Principle 111

IV Perturbation Theory for a Nondegenerate State 113

V The Stark Effect of the Hydrogen Atom 116

VI Perturbation Theory for Degenerate States 119

VII Concluding Remarks 120

VIII Problems 120

10 The Helium Atom 122

I Introduction 122

II Experimental Developments 123

III Pauli’s Exclusion Principle 126

IV The Discovery of the Electron Spin 127

V The Mathematical Description of the Electron Spin 129

VI The Exclusion Principle Revisited 132

VII Two-electron Systems 133

VIII The Helium Atom 135

IX The Helium Atom Orbitals 138

X Concluding Remarks 139

XI Problems 140

11 Atomic Structure 142

I Introduction 142

II Atomic and Molecular Wave Function 145

III The Hartree-Fock Method 146

IV Slater Orbitals 152

V Multiplet Theory 154

VI Concluding Remarks 158

VII Problems 158

12 Molecular Structure 160

I Introduction 160

II The Born-Oppenheimer Approximation 161

III Nuclear Motion of Diatomic Molecules 164

IV The Hydrogen Molecular Ion 169

V The Hydrogen Molecule 173

VI The Chemical Bond 176

VII The Structures of Some Simple Polyatomic Molecules 179

VIII The Hückel Molecular Orbital Method 183

IX Problems 189

Index 191

"…the treatment of individual topics and concepts is very good and informative…" (Journal of Chemical Education, January 2005)

"…this book serves as a skeletal summary of arguments presented in class...” (CHOICE, October 2004)

HENDRIK F. HAMEKA is Professor of Theoretical Chemistry in the Department of Chemistry at the University of Pennsylvania. Originally trained as a theoretical physicist, he studied quantum mechanics under H. A. Kramers (who in turn had studied under Niels Bohr). This study sparked his interest in chemical applications of quantum mechanics, which subsequently became his principal research specialty. He has written four previous textbooks on this subject, the last of which was published by Wiley. A unique introductory text on quantum mechanics

Albert Einstein famously expressed his dismay at the implications of quantum mechanics (QM) when he protested, "God does not play dice with the universe." Theology aside, QM theory has held up as a scientific explanation of matter and radiation at the atomic level. Along with Einstein’s Theory of General Relativity, QM comprises the backbone of modern physics and plays a majo role in our understanding of chemistry.

Quantum Mechanics: A Conceptual Approach offers students an easy-to-understand introduction to this essential field. Assuming no prior knowledge on the part of its reader, this text emphasizes the basic concepts that provide a solid foundation for the future study of quantum chemistry. Beginning with a description of the historical developments that led to the discovery of QM, a feature often neglected in other texts, Quantum Mechanics moves on to cover:

• Mathematics of QM Applications
• Classical mechanics
• The hydrogen atom
• Wave mechanics of a free particle
• Atomic structure
• The Schrödinger equation
• Molecular structure

Written in a student-friendly style by experienced author and professor Hendrik Hameka, this text also includes problem sets to reinforce the concepts outlined. Both comprehensive and accessible, Quantum Mechanics: A Conceptual Approach provides all those interested in the field with an invaluable introduction to this important topic.