Supersymmetry in quantum mechanics / Fred Cooper, Avinash Khare, Uday Sukhatme.

Format:

Book

Author/Creator:

Cooper, Fred, 1944-

Contributor:

Khare, Avinash.

Sukhatme, Uday.

Language:

English

Subjects (All):

Supersymmetry.

Physical Description:

xi, 210 pages : illustrations ; 23 cm

Place of Publication:

Singapore ; River Edge, NJ : World Scientific, [2001]

Summary:

For advanced undergraduate and graduate courses in quantum mechanics, this text provides an elementary description of supersymmetry, a conceptual framework for understanding potential problems in quantum mechanics using ideas borrowed from quantum field theory. Rather than aiming for comprehensive coverage, the authors include what they consider the most important supersymmetry topics to complement traditional quantum mechanics texts. c. Book News Inc.

Contents:

Chapter 2 The Schrodinger Equation in One Dimension 7

2.1 General Properties of Bound States 8

2.2 General Properties of Continuum States and Scattering 9

2.3 The Harmonic Oscillator in the Operator Formalism 10

Chapter 3 Factorization of a General Hamiltonian 15

3.1 Broken Supersymmetry 23

3.2 SUSY Harmonic Oscillator 28

3.3 Factorization and the Hierarchy of Hamiltonians 30

Chapter 4 Shape Invariance and Solvable Potentials 35

4.1 General Formulas for Bound State Spectrum, Wave Functions and S-Matrix 36

4.2 Strategies for Categorizing Shape Invariant Potentials 38

4.2.1 Solutions Involving Translation 38

4.2.2 Solutions Involving Scaling 47

4.2.3 Other Solutions 53

4.3 Shape Invariance and Noncentral Solvable Potentials 56

Chapter 5 Charged Particles in External Fields and Supersymmetry 61

5.1 Spinless Particles 61

5.2 Non-relativistic Electrons and the Pauli Equation 62

5.3 Relativistic Electrons and the Dirac Equation 68

5.4 SUSY and the Dirac Equation 70

5.5 Dirac Equation with a Lorentz Scalar Potential in 1+1 Dimensions 72

5.6 Supersymmetry and the Dirac Particle in a Coulomb Field 75

5.7 SUSY and the Dirac Particle in a Magnetic Field 78

Chapter 6 Isospectral Hamiltonians 81

6.1 One Parameter Family of Isospectral Potentials 82

6.2 Generalization to n-Parameter Isospectral Family 84

6.3 Inverse Scattering and Solitons 88

Chapter 7 New Periodic Potentials from Supersymmetry 97

7.1 Unbroken SUSY and the Value of the Witten Index 97

7.2 Lame Potentials and Their Supersymmetric Partners 101

7.3 Associated Lame Potentials and Their Supersymmetric Partners 110

7.3.1 a = b = Integer 113

Chapter 8 Supersymmetric WKB Approximation 119

8.1 Lowest Order WKB Quantization Condition 120

8.1.1 Simpler Approach for the Lowest Order Quantization Condition 122

8.2 Some General Comments on WKB Theory 124

8.3 Tunneling Probability in the WKB Approximation 125

8.4 SWKB Quantization Condition for Unbroken Supersymmetry 126

8.5 Exactness of the SWKB Condition for Shape Invariant Potentials 128

8.6 Comparison of the SWKB and WKB Approaches 130

8.7 SWKB Quantization Condition for Broken Supersymmetry 131

8.8 Tunneling Probability in the SWKB Approximation 132

Chapter 9 Perturbative Methods for Calculating Energy Spectra and Wave Functions 137

9.1 Variational Approach 137

9.2 SUSY [delta] Expansion Method 141

9.3 Supersymmetry and Double Well Potentials 143

9.4 Supersymmetry and the Large-N Expansion 150

Appendix A Path Integrals and SUSY 157

A.1 Dirac Notation 157

A.2 Path Integral for the Evolution Operator 158

A.3 Path Integrals for Fermionic Degrees of Freedom 162

A.3.1 Hilbert Space for Fermionic Oscillator 162

A.4 Path Integral Formulation of SUSY Quantum Mechanics 167

A.5 Superspace Formulation of SUSY Quantum Mechanics 174

Appendix B Operator Transforms

New Solvable Potentials from Old 177

B.1 Natanzon Potentials 182

Appendix C Logarithmic Perturbation Theory 185.

Notes:

Includes bibliographical references and index.

ISBN:

9810246056

OCLC:

47870999