Supersymmetric methods in quantum, statistical and solid state physics / Georg Junker.

Junker, Georg, 1961- author.
Standardized Title:
Supersymmetric methods in quantum and statistical physics
Enlarged and revised edition.
Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) : IOP Publishing, [2019]
IOP (Series). Release 6.
IOP expanding physics
[IOP release 6]
IOP expanding physics, 2053-2563
1 online resource (various pagings) : illustrations.
Quantum theory.
Statistical physics.
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Mode of access: World Wide Web.
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Georg Junker is affiliated with both the European Organization for Astronomical Research in the Southern Hemisphere, Garching, Germany and the Institute for Theoretical Physics at the University of Erlangen-Nürnberg, Erlangen, Germany.
As with the earlier edition, this book provides an accessible introduction to supersymmetric quantum mechanics and its applications in quantum, statistical and solid state physics. Building on the earlier edition it now encapsulates the substantial developments that have been made in supersymmetric quantum mechanics in recent years including conditionally exactly solvable systems, models of classical field theory and the many new interesting aspects within the area of stochastic dynamics, the Pauli and Dirac Equation, coherent states and non-linear algebras. Aimed at graduate students and scientists this book provides a thorough review on supersymmetric quantum mechanics and now includes problems and solutions.
1. Introduction
2. Supersymmetric quantum mechanics
2.1. Definition of SUSY quantum mechanics
2.2. Properties of N = 2 SUSY quantum mechanics
2.3. Problems
3. The Witten model
3.1. Witten's model and its modification
3.2. Witten parity and SUSY transformation
3.3. The SUSY potential and zero-energy states
3.4. Broken versus good SUSY
3.5. SUSY transformations for continuum states
3.6. Examples
3.7. Problems
4. One-dimensional quantum systems
4.1. Supersymmetrisation of one-dimensional systems
4.2. Shape-invariance and exact solutions
4.3. The Darboux transformation method
4.4. A SUSY-partner family for the harmonic oscillator
4.5. Classical fields in (1 + 1) dimensions
4.6. Problems
5. Supersymmetric classical mechanics
5.1. Pseudoclassical models
5.2. A supersymmetric classical model
5.3. The classical dynamics
5.4. Discussion of the fermionic phase
5.5. Quantisation
5.6. Problems
6. Quasi-classical approximation
6.1. The path-integral formalism
6.2. Quasi-classical quantisation conditions
6.3. Quasi-classical eigenfunctions
6.4. Discussion of the results
6.5. Problems
7. Supersymmetry in classical stochastic dynamics
7.1. Langevin and Fokker-Planck equation
7.2. Supersymmetry of the Fokker-Planck equation
7.3. Supersymmetry of the Langevin equation
7.4. Implications of supersymmetry
7.5. Continuous stationary Markov processes
7.6. Problems
8. Supersymmetric Pauli Hamiltonians
8.1. Electrons in an external magnetic field
8.2. Pauli paramagnetism of non-interacting electrons
8.3. Electrons in a spherically symmetric scalar field
8.4. Problems
9. Supersymmetric Dirac Hamiltonians
9.1. The Dirac Hamiltonian and SUSY
9.2. The free Dirac Hamiltonian in three dimensions
9.3. The two-dimensional Dirac Hamiltonian with magnetic field
9.4. Dirac Hamiltonians with a Lorentz-scalar potential
9.5. Dirac electrons in spherical symmetric potentials
9.6. Supersymmetry of the Dirac Coulomb Hamiltonian
9.7. The relativistic Witten model
9.8. Problems
10. Concluding remarks and overview.
"Version: 20190101"--Title page verso.
"This is a revised and enlarged edition of the monograph previously published by Springer in 1996 under the slightly shorter title Supersymmetric methods in quantum and statistical physics"--Page xi.
Includes bibliographical references.
Title from PDF title page (viewed on February 4, 2019).
Institute of Physics (Great Britain), publisher.
Other format:
Print version:
Publisher Number:
10.1088/2053-2563/aae6d5 doi
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Restricted for use by site license.
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