This book gives an introduction to supersymmetric quantum mechanics and a comprehensive review of its applications in quantum and statistical physics. The classical version and the quantum version of Witten's model are studied in detail. Exact spectral properties of the model for the so-called shape invariant potentials are discussed. The quasi-classical quantization rules are derived. The topics covered also include the supersymmetric structure of a classical stochastic dynamical system obeying the Langevin or the Fokker-Planck equation, Pauli's Hamiltonian and its application to the…mehr
This book gives an introduction to supersymmetric quantum mechanics and a comprehensive review of its applications in quantum and statistical physics. The classical version and the quantum version of Witten's model are studied in detail. Exact spectral properties of the model for the so-called shape invariant potentials are discussed. The quasi-classical quantization rules are derived. The topics covered also include the supersymmetric structure of a classical stochastic dynamical system obeying the Langevin or the Fokker-Planck equation, Pauli's Hamiltonian and its application to the paragmagnetism of a non-interacting electron gas in two and three dimensions, supersymmetry of Dirac's Hamiltonian, and others. The book addresses graduate students as well as scientists.
1. Introduction.- 2. Supersymmetric Quantum Mechanics.- 2.1 Definition of SUSY Quantum Mechanics.- 2.2 Properties of N = 2 SUSY Quantum Mechanics.- 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 Examples.- 4. Supersymmetric Classical Mechanics.- 4.1 Pseudoclassical Models.- 4.2 A Supersymmetric Classical Model.- 4.3 The Classical Dynamics.- 4.4 Discussion of the Fermionic Phase.- 4.5 Quantization.- 5. Exact Solution of Eigenvalue Problems.- 5.1 Supersymmetrization of One-Dimensional Systems.- 5.2 Shape-Invariance and Exact Solutions.- 6. Quasi-Classical Path-Integral Approach.- 6.1 The Path-Integral FormaHsm.- 6.2 Quasi-Classical Quantization Conditions..- 6.3 Quasi-Classical Eigenfunctions.- 6.4 Discussion of the Results.- 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.- 8. Supersymmetry in the Pauli and Dirac Equation.- 8.1 Pauli's Hamiltonian in Two and Three Dimensions.- 8.2 Pauli Paramagnetism of Non-Interacting Electrons, Revisited..- 8.3 The Dirac Hamiltonian and SUSY.- 9. Concluding Remarks and Overview.- References.- Symbols.- Name Index.
1. Introduction.- 2. Supersymmetric Quantum Mechanics.- 2.1 Definition of SUSY Quantum Mechanics.- 2.2 Properties of N = 2 SUSY Quantum Mechanics.- 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 Examples.- 4. Supersymmetric Classical Mechanics.- 4.1 Pseudoclassical Models.- 4.2 A Supersymmetric Classical Model.- 4.3 The Classical Dynamics.- 4.4 Discussion of the Fermionic Phase.- 4.5 Quantization.- 5. Exact Solution of Eigenvalue Problems.- 5.1 Supersymmetrization of One-Dimensional Systems.- 5.2 Shape-Invariance and Exact Solutions.- 6. Quasi-Classical Path-Integral Approach.- 6.1 The Path-Integral FormaHsm.- 6.2 Quasi-Classical Quantization Conditions..- 6.3 Quasi-Classical Eigenfunctions.- 6.4 Discussion of the Results.- 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.- 8. Supersymmetry in the Pauli and Dirac Equation.- 8.1 Pauli's Hamiltonian in Two and Three Dimensions.- 8.2 Pauli Paramagnetism of Non-Interacting Electrons, Revisited..- 8.3 The Dirac Hamiltonian and SUSY.- 9. Concluding Remarks and Overview.- References.- Symbols.- Name Index.
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