Cover
Half Title
Title Page
Copyright Page
Table of contents
Preface to the first edition
Preface to the second edition
Preface to the third edition
Author
1 Waves and Particles
1.1 Introduction
1.2 Light as ParticlesโThe Photoelectric Effect
1.3 Electrons as Waves
1.4 Reality and Causality
1.5 Connection to the Classical World
1.5.1 Position and Momentum
1.5.2 Noncommuting Operators
1.5.3 Another View
1.5.4 Wave Packets
1.6 Summary
References
Problems
2 The Schrรถdinger Equation
2.1 Waves and the Differential Equation
2.1.1 The Free Particle
2.1.2 A Potential Step
Case I. E < V0
Case II. E > V0
2.2 Density and Current
2.3 The Potential Well
2.3.1 The Infinite Potential Well
2.3.2 The Finite Potential Well
Case I. 0 < E < V0
Case II. E > V0
2.4 The Triangular Well
2.5 Uncertainty
2.6 Numerical Solutions of the Schrรถdinger Equation
References
Problems
3
Tunneling
3.1 The Tunnel Barrier
3.1.1 The Simple Rectangular Barrier
3.1.2 A More Complex Barrier
3.2 The Double Barrier
3.2.1 Simple, Equal Barriers
3.2.2 The Unequal-Barrier Case
3.2.3 Shape of the Resonance
3.3 Approximation MethodsโThe WKB Method
3.3.1 Bound States of a General Potential
3.3.2 Tunneling
3.4 Tunneling Devices
3.4.1 The Landauer Formulation
3.4.2 The Esaki Diode
3.4.3 The Resonant Tunneling Diode
3.4.4 Single-Electron Tunneling
3.4.5 Josephson Tunneling
References
Problems
4 Periodic Potentials
4.1 Atoms on a Lattice
4.2 Another Approach
4.3 Bonds and Bands
4.4 Electron PairingโSuperconductivity
4.4.1 Observable Properties
4.4.2 Pairing and Gaps
References
Problems
5 The Harmonic Oscillator
5.1 The Wave Functions
5.2 The LC-Circuit
5.3 An Atomic Lattice and Phonons
5.4 Motion in a Quantizing Magnetic Field
5.4.1 Connection with the Classical Orbit
5.4.2 Adding Lateral Confinement
5.4.3 The Quantum Hall Effect
5.5 The Modern Standard Unit System
References
Problems
6 Operators and Bases
6.1 Time Dependence of Operators
6.2 Linear Vector Spaces
6.2.1 Hermitian Operators
6.2.2 Some Matrix Properties
6.2.3 The Eigenvalue Problem
6.3 Supersymmetry
6.4 The Density Matrix
6.5 The Wigner Function
References
Problems
7 Stationary Perturbation Theory
7.1 The Perturbation Series
7.2 Some Examples of Perturbation Theory
7.2.1 The Stark Effect in a Potential Well
7.2.2 The Shifted Harmonic Oscillator
7.2.3 Multiple Quantum Wells
7.3 An Alternative ApproachโThe Variational Method
Problems
8 Time-Dependent Perturbation Theory
8.1 The Perturbation Series
8.2 The Interaction Representation
8.3 Exponential Decay
8.4 The Lippmann-Schwinger Equation
8.4.1 The Scattering State T-Matrix
8.4.2 Gaining the Lippmann-Schwinger Equation
8.4.3 Orthogonality of the Scattering States
References
Problems
9 Motion in Centrally Symmetric Potentials
9.1 The Two-Dimensional Harmonic Oscillator
9.1.1 Rectangular Coordinates
9.1.2 Polar Coordinates and Angular Momentum
9.1.3 Splitting the Angular Momentum States with a Magnetic Field
9.2 The Hydrogen Atom
9.2.1 The Radial Equation
9.2.2 Angular Solutions
9.2.3 Angular Momentum Again
9.2.4 Atomic Energy Levels
9.3 The Covalent Bond in Semiconductors
9.4 Hydrogenic Impurities in Semiconductors
References
Problems
10 Spin Angular Momentum
10.1 Spin Angular Momentum
10.2 Two-Level Systems
10.3 Systems of Identical Particles
10.4 Spin Effects in Semiconductors
10.4.1 The Spin-Orbit Interaction
10.4.2 Bulk Inversion Asymmetry
10.4.3 Structural Inversion Asymmetry
References
Problems
11 An Introduction to Quantum Computing
11.1 Qubits and Entanglement
11.1.1 Bits and Qubits
11.1.2 Entanglement
11.2 The Jaynes-Cummings Model
11.3 Quantum Dots for Qubits
11.3.1 31P Donors
11.3.2 Double Quantum Dots
11.3.3 NV Centers
11.4 Josephson Junctions
11.4.1 The SQUID
11.4.2 Charge Qubits
11.4.3 Flux Qubits
11.4.4 The Hybrid Charge-Flux Qubit
11.5 Optical Qubits
References
Solutions to Selected Problems
Index