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Quantum Mechanics: For Electrical Engineers by Isaak D Mayergoyz

The book is designed for a one-semester graduate course in quantum mechanics for electrical engineers. It can also be used for teaching quantum mechanics to graduate students in materials science and engineering departments as well as to applied physicists. The selection of topics in the book is based on their relevance to engineering applications. The book provides the theoretical foundation for graduate courses in quantum optics and lasers, semiconductor electronics, applied superconductivity and quantum computing. It covers (along with traditional subjects) the following topics: resonant and Josephson tunneling; Landau levels and their relation to the integer quantum Hall effect; effective mass Schrodinger equation and semi-classical transport; quantum transitions in two-level systems; Berry phase and Berry curvature; density matrix and optical Bloch equation for two-level systems; Wigner function and quantum transport; exchange interaction and spintronic.

Product Details

ISBN-13: 9789813148017
Publisher: World Scientific Publishing Company, Incorporated
Publication date: 09/23/2016
Pages: 312
Sales rank: 857,298
Product dimensions: 6.00(w) x 8.90(h) x 0.60(d)

Table of Contents

Preface vii

1 Basics of Lagrangian and Hamiltonian Mechanics 1

1.1 What is Quantum Mechanics 1

1.2 The Principle of Least Action and Lagrange Equations 3

1.3 Conservation Laws 9

1.4 Hamiltonian Equations and Poisson Brackets 14

Problems 20

2 Fundamentals of Quantum Mechanics 23

2.1 Hilbert Space and Hermitian Operators 23

2.2 Postulates of Quantum Mechanics 32

2.3 Operators of Coordinates and Momentum 42

2.4 Angular Momentum Operators 51

2.5 Hamiltonian Operator 63

Problems 73

3 Tunneling 75

3.1 Tunneling Through a Rectangular Barrier 75

3.2 Resonant Tunneling 84

3.3 Josephson Tunneling in Superconductors 91

Problems 102

4 Problems with Discrete Energy Spectrum 103

4.1 The Potential Well 103

4.2 The Harmonic Oscillator 114

4.3 The Hydrogen Atom 127

4.4 Landau Levels Quantum Hall Effect 137

4.5 Model Problem for Energy Gap Formation in Superconductors 147

Problems 157

5 Periodic Potentials 159

5.1 Bloch Function and Energy Bands 159

5.2 Kronig-Penney Model 167

5.3 Effective Mass Schrodinger Equation and Semiclassical Transport 173

Problems 182

6 Matrix Form of Quantum Mechanics. Perturbation Theory. Density Matrix 183

6.1 Matrix Form of Quantum Mechanics 183

6.2 Time-Independent Perturbation Theory 196

6.3 Time-Dependent Perturbations. Adiabatic Perturbations and Berry's Phase 209

6.4 Density Matrix. Optical Bloch Equation. Wigner Function and Quantum Transport 225

Problems 237

7 Spin. Identical Particles. Second Quantization. Quantization of Electromagnetic Field 239

7.1 Spin 239

7.2 Identical Particles. Exchange Interaction 254

7.3 Second Quantization. (Representation of Occupation Numbers) 270

7.4 Quantization of Electromagnetic Field 280

Problems 292

Bibliography 295

Index 297

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