Fundamentals of quantum mechanics : for solid state electronics and optics / C.L. Tang.

Format:

Book

Author/Creator:

Tang, C. L. (Chung Liang), 1934-

Language:

English

Subjects (All):

Quantum theory.

Physical Description:

xii, 208 pages : illustrations ; 26 cm

Place of Publication:

Cambridge, UK ; New York : Cambridge University Press, 2005.

Summary:

Quantum mechanics has evolved from a subject of study in pure physics to one with a wide range of applications in many diverse fields. The basic concepts of quantum mechanics are explained in this book in a concise and easy-to-read manner, leading toward applications in solid-state electronics and modern optics. Following a logical sequence, the book focuses on key ideas and is conceptually and mathematically self-contained. The fundamental principles of quantum mechanics are illustrated by showing their application to systems such as the hydrogen atom, multi-electron ions and atoms, the formation of simple organic molecules, and crystalline solids of practical importance. It leads on from these basic concepts to discuss some of the most significant applications in modern semiconductor electronics and optics.

Containing many homework problems, the book is suitable for seniorlevel undergraduate and graduate-level students in electrical engineering, material sciences, applied physics and chemistry.

Contents:

1 Classical mechanics vs. quantum mechanics 1

1.1 Brief overview of classical mechanics 1

1.2 Overview of quantum mechanics 2

2 Basic postulates and mathematical tools 8

2.1 State functions (Postulate 1) 8

2.2 Operators (Postulate 2) 12

2.3 Equations of motion (Postulate 3) 18

2.4 Eigen functions, basis states, and representations 21

2.5 Alternative notations and formulations 23

3 Wave/particle duality and de Broglie waves 33

3.1 Free particles and de Broglie waves 33

3.2 Momentum representation and wave packets 37

4 Particles at boundaries, potential steps, barriers, and in quantum wells 40

4.1 Boundary conditions and probability currents 40

4.2 Particles at a potential step, up or down 43

4.3 Particles at a barrier and the quantum mechanical tunneling effect 47

4.4 Quantum wells and bound states 50

4.5 Three-dimensional potential box or quantum well 59

5 The harmonic oscillator and photons 63

5.1 The harmonic oscillator based on Heisenberg's formulation of quantum mechanics 63

5.2 The harmonic oscillator based on Schrodinger's formalism 70

5.3 Superposition state and wave packet oscillation 73

5.4 Photons 75

6 The hydrogen atom 86

6.1 The Hamiltonian of the hydrogen atom 86

6.2 Angular momentum of the hydrogen atom 87

6.3 Solution of the time-independent Schrodinger equation for the hydrogen atom 94

6.4 Structure of the hydrogen atom 97

6.5 Electron spin and the theory of generalized angular momentum 101

6.6 Spin-orbit interaction in the hydrogen atom 106

7 Multi-electron ions and the periodic table 110

7.1 Hamiltonian of the multi-electron ions and atoms 110

7.2 Solutions of the time-independent Schrodinger equation for multielectron ions and atoms 112

7.3 The periodic table 115

8 Interaction of atoms with electromagnetic radiation 119

8.1 Schrodinger's equation for electric dipole interaction of atoms with electromagnetic radiation 119

8.2 Time-dependent perturbation theory 120

8.3 Transition probabilities 122

8.4 Selection rules and the spectra of hydrogen atoms and hydrogen-like ions 126

8.5 The emission and absorption processes 128

8.6 Light Amplification by Stimulated Emission of Radiation (LASER) and the Einstein A- and B-coefficients 130

9 Simple molecular orbitals and crystalline structures 135

9.1 Time-independent perturbation theory 135

9.2 Covalent bonding of diatomic molecules 139

9.3 sp, sp[superscript 2], and sp[superscript 3] orbitals and examples of simple organic molecules 144

9.4 Diamond and zincblende structures and space lattices 148

10 Electronic properties of semiconductors and the p-n junction 151

10.1 Molecular orbital picture of the valence and conduction bands of semiconductors 151

10.2 Nearly-free-electron model of solids and the Bloch theorem 153

10.3 The k-space and the E vs. k diagram 157

10.4 Density-of-states and the Fermi energy for the free-electron gas model 163

10.5 Fermi-Dirac distribution function and the chemical potential 164

10.6 Effective mass of electrons and holes and group velocity in semiconductors 170

10.7 n-type and p-type extrinsic semiconductors 173

10.8 The p-n junction 176

11 The density matrix and the quantum mechanic Boltzmann equation 182

11.1 Definitions of the density operator and the density matrix 182

11.2 Physical interpretation and properties of the density matrix 183

11.3 The density matrix equation or the quantum mechanic Boltzmann equation 186

11.4 Examples of the solutions and applications of the density matrix equations 188.

Notes:

Includes bibliographical references (page 204) and index.

ISBN:

0521829526

OCLC:

57574521

Publisher Number:

9780521829526 (hbk.)