Table of Contents
Preface to the EAP Series ix
Preface to Quantum Mechanics: Lecture notes xii
Acknowledgments xiii
Notation xiv
1 Introduction 1-1
1.1 Experimental motivations 1-1
1.2 Wave mechanics postulates 1-8
1.3 Postulates' discussion 1-13
1.4 Continuity equation 1-15
1.5 Eigenstates and eigenvalues 1-18
1.6 Time evolution 1-21
1.7 Spatial dependence 1-23
1.8 Dimensionality reduction 1-27
1.9 Problems 1-30
References 1-32
2 1D wave mechanics 2-1
2.1 Basic relations 2-1
2.2 Free particle: wave packets 2-4
2.3 Particle reflection and tunneling 2-12
2.4 Motion in soft potentials 2-20
2.5 Resonant tunneling, and metastable states 2-30
2.6 Localized state coupling, and quantum oscillations 2-40
2.7 Periodic systems: energy bands and gaps 2-49
2.8 Periodic systems: particle dynamics 2-63
2.9 Harmonic oscillator: brute force approach 2-73
2.10 Problems 2-79
References 2-87
3 Higher dimensionality effects 3-1
3.1 Quantum interference and the AB effect 3-1
3.2 Landau levels and quantum Hall effect 3-12
3.3 Scattering and diffraction 3-17
3.4 Energy bands in higher dimensions 3-27
3.5 Axially-symmetric systems 3-35
3.6 Spherically-symmetric systems: brute force approach 3-42
3.7 Atoms 3-51
3.8 Spherically-symmetric scatterers 3-61
3.9 Problems 3-65
References 3-72
4 Bra-ket formalism 4-1
4.1 Motivation 4-1
4.2 States, state vectors, and linear operators 4-4
4.3 State basis and matrix representation 4-10
4.4 Change of basis, and matrix diagonalization 4-16
4.5 Observables: expectation values and uncertainties 4-27
4.6 Quantum dynamics: three pictures 4-33
4.7 Coordinate and momentum representations 4-45
4.8 Problems 4-55
5 Some exactly solvable problems 5-1
5.1 Two-level systems 5-1
5.2 The Ehrenfest theorem 5-8
5.3 The Feynman path integral 5-11
5.4 Revisiting harmonic oscillator 5-18
5.5 Glauber states and squeezed states 5-25
5.6 Revisiting spherically-symmetric systems 5-35
5.7 Spin and its addition to orbital angular momentum 5-40
5.8 Problems 5-47
References 5-53
6 Perturbative approaches 6-1
6.1 Eigenproblems 6-1
6.2 The Stark effect 6-7
6.3 Fine structure of atomic levels 6-10
6.4 The Zeeman effect 6-16
6.5 Time-dependent perturbations 6-20
6.6 Quantum-mechanical golden rule 6-27
6.7 Golden rule for step-like perturbations 6-34
6.8 Problems 6-38
References 6-42
7 Open quantum systems 7-1
7.1 Open systems, and the density matrix 7-1
7.2 Coordinate representation, and the Wigner function 7-8
7.3 Open system dynamics: dephasing 7-16
7.4 Fluctuation-dissipation theorem 7-22
7.5 The Heisenberg-Langevin approach 7-35
7.6 Density matrix approach 7-39
7.7 Problems 7-58
References 7-60
8 Multiparticle systems 8-1
8.1 Distinguishable and indistinguishable particles 8-1
8.2 Singlets, triplets, and the exchange interaction 8-5
8.3 Multiparticle systems 8-14
8.4 Perturbative approaches 8-27
8.5 Quantum computation and cryptography 8-33
8.6 Problems 8-55
References 8-60
9 Introduction to relativistic quantum mechanics 9-1
9.1 Electromagnetic field quantization 9-1
9.2 Photon absorption and counting 19-8
9.3 Photon emission: spontaneous and stimulated 9-15
9.4 Cavity QED 9-20
9.5 The Klein-Gordon and relativistic Schrodinger equations 9-25
9.6 Dirac's theory 9-29
9.7 Low-energy limit 9-33
9.8 Problems 9-39
References 9-41
10 Making sense of quantum mechanics 10-1
10.1 Quantum measurements 10-1
10.2 QND measurements 10-7
10.3 Hidden variables and local reality 10-12
10.4 Interpretations of quantum mechanics 10-18
Reference 10-19
Appendices
A Selected mathematical formulas A-1
B Selected physical constants B-1
Bibliography 13-1
