Fundamentals of Quantum Mechanics for Solid State Electronics, Optics

Cover......Page 1
Title Page......Page 4
ISBN: 0521829526, 051112595x......Page 5
Contents......Page 8
Preface......Page 11
1.1 Brief overview of classical mechanics......Page 14
1.2 Overview of quantum mechanics......Page 15
Further reading......Page 19
2.1 State functions (Postulate 1)......Page 21
2.2 Operators (Postulate 2)......Page 25
2.3 Equations of motion (Postulate 3)......Page 31
2.4 Eigen functions, basis states, and representations......Page 34
2.5 Alternative notations and formulations......Page 36
Concluding remarks......Page 43
2.6 Problems......Page 44
3.1 Free particles and de Broglie waves......Page 46
3.2 Momentum representation and wave packets......Page 50
3.3 Problems......Page 52
4.1 Boundary conditions and probability currents......Page 53
4.2 Particles at a potential step, up or down......Page 56
4.3 Particles at a barrier and the quantum mechanical tunneling effect......Page 60
4.4 Quantum wells and bound states......Page 63
4.5 Three-dimensional potential box or quantum well......Page 72
4.6 Problems......Page 73
5.1 The harmonic oscillator based on Heisenberg’s formalism of quantum mechanics......Page 76
5.2 The harmonic oscillator based on Schro¨ dinger’s formalism......Page 83
5.3 Superposition state and wave packet oscillation......Page 86
5.4 Photons......Page 88
5.5 Problems......Page 97
6.1 The Hamiltonian of the hydrogen atom......Page 99
6.2 Angular momentum of the hydrogen atom......Page 100
6.3 Solution of the time-independent Schro¨ dinger equation for the hydrogen atom......Page 107
6.4 Structure of the hydrogen atom......Page 110
6.5 Electron spin and the theory of generalized angular momentum......Page 114
6.6 Spin–orbit interaction in the hydrogen atom......Page 119
6.7 Problems......Page 121
7.1 Hamiltonian of the multi-electron ions and atoms......Page 123
7.2 Solutions of the time-independent Schro¨ dinger equation for multi-electron ions and atoms......Page 125
7.3 The periodic table......Page 128
7.4 Problems......Page 131
8.1 Schro¨ dinger’s equation for electric dipole interaction of atoms with electromagnetic radiation......Page 132
8.2 Time-dependent perturbation theory......Page 133
8.3 Transition probabilities......Page 135
8.4 Selection rules and the spectra of hydrogen and hydrogen-like ions......Page 139
8.5 The emission and absorption processes......Page 141
8.6 Light Amplification by Stimulated Emission of Radiation (LASER) and the Einstein A- and B-coefficients......Page 143
8.7 Problems......Page 146
9.1 Time-independent perturbation theory......Page 148
9.2 Covalent bonding of diatomic molecules......Page 152
9.3 sp, sp2 and sp3 orbitals and examples of simple organic molecules......Page 157
9.4 Diamond and zincblende structures and space lattices......Page 161
9.5 Problems......Page 162
10.1 Molecular orbital picture of the valence and conduction bands of semiconductors......Page 164
10.2 Nearly-free-electron model of solids and the Bloch theorem......Page 166
10.3 The k-space and the E vs. k diagram......Page 170
10.4 Density-of-states and the Fermi energy for the free-electron gas model......Page 176
10.5 Fermi–Dirac Distribution function and the chemical potential......Page 177
10.6 Effective mass of electrons and holes and group velocity in semiconductors......Page 183
10.7 n-type and p-type extrinsic semiconductors......Page 186
10.8 The p–n junction......Page 189
10.9 Problems......Page 193
11.1 Definitions of the density operator and the density matrix......Page 195
11.2 Physical interpretation and properties of the density matrix......Page 196
11.3 The density matrix equation or the quantum mechanic Boltzmann equation......Page 199
11.4 Examples of the solutions and applications of the density-matrix equations......Page 201
11.5 Problems......Page 215
References......Page 217
Index......Page 218