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书名：	Supersymmetry in Quantum Mechanics
作者：	Cooper, Fred; Khare, Avinash; Sukhatme, Uday
出版时间：	2001-06-29
ISBN：	9789810246051(P-ISBN) ，9789812386502(O-ISBN)
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摘要：

书目详情：

Contents Preface Chapter 1 Introduction Chapter 2 The Schrodinger Equation in One Dimension 2.1 General Properties of Bound States 2.2 General Properties of Continuum States and Scattering 2.3 The Harmonic Oscillator in the Operator Formalism Chapter 3 Factorization of a General Hamiltonian 3.1 Broken Supersymmetry 3.2 SUSY Harmonic Oscillator 3.3 Factorization and the Hierarchy of Hamiltonians Chapter 4 Shape Invariance and Solvable Potentials 4.1 General Formulas for Bound State Spectrum, Wave Functions and S-Matrix 4.2 Strategies for Categorizing Shape Invariant Potentials 4.2.1 Solutions Involving Translation 4.2.2 Solutions Involving Scaling 4.2.3 Other Solutions 4.3 Shape Invariance and Noncentral Solvable Potentials Chapter 5 Charged Particles in External Fields and Supersymmetry 5.1 Spinless Particles 5.2 Non-relativistic Electrons and the Pauli Equation 5.3 Relativistic Electrons and the Dirac Equation 5.4 SUSY and the Dirac Equation 5.5 Dirac Equation with a Lorentz Scalar Potential in 1 + 1 Dimensions 5.6 Supersymmetry and the Dirac Particle in a Coulomb Field 5.7 SUSY and the Dirac Particle in a Magnetic Field Chapter 6 Isospectral Hamiltonians 6.1 One Parameter Family of Isospectral Potentials 6.2 Generalization to n-Parameter Isospectral Family 6.3 Inverse Scattering and Solitons Chapter 7 New Periodic Potentials from Supersymmetry 7.1 Unbroken SUSY and the Value of the Witten Index 7.2 Lame Potentials and Their Supersymmetric Partners 7.3 Associated Lame Potentials and Their Supersymmetric Partners 7.3.1 a = b = Integer Chapter 8 Supersymmetric WKB Approximation 8.1 Lowest Order WKB Quantization Condition 8.1.1 Simpler Approach for the Lowest Order Quantization Condition 8.2 Some General Comments on WKB Theory 8.3 Tunneling Probability in the WKB Approximation 8.4 SWKB Quantization Condition for Unbroken Supersymmetry 8.5 Exactness of the SWKB Condition for Shape Invariant Potentials 8.6 Comparison of the SWKB and WKB Approaches 8.7 SWKB Quantization Condition for Broken Supersymmetry 8.8 Tunneling Probability in the SWKB Approximation Chapter 9 Perturbative Methods for Calculating Energy Spectra and Wave Functions 9.1 Variational Approach 9.2 SUSY d Expansion Method 9.3 Supersymmetry and Double Well Potentials 9.4 Supersymmetry and the Large-N Expansion Appendix A Path Integrals and SUSY A.1 Dirac Notation A.2 Path Integral for the Evolution Operator A.3 Path Integrals for Fermionic Degrees of Freedom A.3.1 Hilbert Space for Fermionic Oscillator A.4 Path Integral Formulation of SUSY Quantum Mechanics A.5 Superspace Formulation of SUSY Quantum Mechanics Appendix B Operator Transforms - New Solvable Potentials from Old B.1 Natanzon Potentials Appendix C Logarithmic Perturbation Theory Appendix D Solutions to Problems Index

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