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
