Quantum Mechanics: Lecture notes, is intended to be the basis for a two-semester, graduate-level course. It starts with coverage of numerous wave-mechanical effects in one- and multi-dimensional systems (including the energy band theory), and then proceeds to the bra–ket formalism necessary for the discussion of more advanced topics, including particle spin, and open and multi-particle quantum systems. The book also includes a section on quantum computation and cryptography, and it ends with a special chapter on quantum measurements and interpretations of quantum mechanics.
Author(s): Konstantin K. Likharev
Series: Essential Advanced Physics, 5
Publisher: IOP Publishing
Year: 2019
Language: English
Pages: 450
City: Bristol
PRELIMS.pdf
Preface to the EAP Series
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Essential Advanced Physics
Distinguishing features of this series—in brief
Level and prerequisites
Origins and motivation
Style
Disclaimer and encouragement
Preface to
Acknowledgments
Notation
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Prime signs
Parts of the series
Appendices
Formulas
CH001.pdf
Chapter 1 Introduction
1.1 Experimental motivations
1.2 Wave mechanics postulates
1.3 Postulates’ discussion
1.4 Continuity equation
1.5 Eigenstates and eigenvalues
1.6 Time evolution
1.7 Spatial dependence
1.8 Dimensionality reduction
1.9 Problems
References
CH002.pdf
Chapter 2 1D wave mechanics
2.1 Basic relations
2.2 Free particle: wave packets
2.3 Particle reflection and tunneling
2.4 Motion in soft potentials
2.5 Resonant tunneling, and metastable states
2.6 Localized state coupling, and quantum oscillations
2.7 Periodic systems: energy bands and gaps
2.8 Periodic systems: particle dynamics
2.9 Harmonic oscillator: brute force approach
2.10 Problems
References
CH003.pdf
Chapter 3 Higher dimensionality effects
3.1 Quantum interference and the AB effect
3.2 Landau levels and quantum Hall effect
3.3 Scattering and diffraction
3.4 Energy bands in higher dimensions
3.5 Axially-symmetric systems
3.6 Spherically-symmetric systems: brute force approach
3.7 Atoms
3.8 Spherically-symmetric scatterers
3.9 Problems
References
CH004.pdf
Chapter 4 Bra–ket formalism
4.1 Motivation
4.2 States, state vectors, and linear operators
4.3 State basis and matrix representation
4.4 Change of basis, and matrix diagonalization
4.5 Observables: expectation values and uncertainties
4.6 Quantum dynamics: three pictures
4.7 Coordinate and momentum representations
4.8 Problems
CH005.pdf
Chapter 5 Some exactly solvable problems
5.1 Two-level systems
5.2 The Ehrenfest theorem
5.3 The Feynman path integral
5.4 Revisiting harmonic oscillator
5.5 Glauber states and squeezed states
5.6 Revisiting spherically-symmetric systems
5.7 Spin and its addition to orbital angular momentum
5.8 Problems
References
CH006.pdf
Chapter 6 Perturbative approaches
6.1 Eigenproblems
6.2 The Stark effect
6.3 Fine structure of atomic levels
6.4 The Zeeman effect
6.5 Time-dependent perturbations
6.6 Quantum-mechanical golden rule
6.7 Golden rule for step-like perturbations
6.8 Problems
References
CH007.pdf
Chapter 7 Open quantum systems
7.1 Open systems, and the density matrix
7.2 Coordinate representation, and the Wigner function
7.3 Open system dynamics: dephasing
7.4 Fluctuation–dissipation theorem
7.5 The Heisenberg–Langevin approach
7.6 Density matrix approach
7.7 Problems
References
CH008.pdf
Chapter 8 Multiparticle systems
8.1 Distinguishable and indistinguishable particles
8.2 Singlets, triplets, and the exchange interaction
8.3 Multiparticle systems
8.4 Perturbative approaches
8.5 Quantum computation and cryptography
8.6 Problems
References
CH009.pdf
Chapter 9 Introduction to relativistic quantum mechanics
9.1 Electromagnetic field quantization
9.2 Photon absorption and counting
9.3 Photon emission: spontaneous and stimulated
9.4 Cavity QED
9.5 The Klein–Gordon and relativistic Schrödinger equations
9.6 Dirac’s theory
9.7 Low-energy limit
9.8 Problems
References
CH010.pdf
Chapter 10 Making sense of quantum mechanics
10.1 Quantum measurements
10.2 QND measurements
10.3 Hidden variables and local reality
10.4 Interpretations of quantum mechanics
References
APP1.pdf
Chapter
A.1 Constants
A.2 Combinatorics, sums, and series
A.3 Basic trigonometric functions
A.4 General differentiation
A.5 General integration
A.6 A few 1D integrals55A powerful (and free) interactive online tool for working out indefinite 1D integrals is available at http://integrals.wolfram.com/index.jsp.
A.7 3D vector products
A.8 Differentiation in 3D Cartesian coordinates
A.9 The Laplace operator ∇2 ≡ ∇ · ∇
A.10 Operators ∇ and ∇2 in the most important systems of orthogonal coordinates1111Some other orthogonal curvilinear coordinate systems are discussed in Part EM, section 2.3.
A.11 Products involving ∇
A.12 Integro-differential relations
A.13 The Kronecker delta and Levi-Civita permutation symbols
A.14 Dirac’s delta-function, sign function, and theta-function
A.15 The Cauchy theorem and integral
A.16 Literature
References
APP2.pdf
Chapter
References
BIBLIO.pdf
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Part EM: Classical Electrodynamics
Part SM: Statistical Mechanics
Multidisciplinary/specialty
