Supersymmetry in Quantum Mechanics.
Başlık:
Supersymmetry in Quantum Mechanics.
Yazar:
Cooper, Fred.
ISBN:
9789812386502
Yazar Ek Girişi:
Fiziksel Tanımlama:
1 online resource (223 pages)
İçerik:
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.
Özet:
This invaluable book provides an elementary description of supersymmetric quantum mechanics which complements the traditional coverage found in the existing quantum mechanics textbooks. It gives physicists a fresh outlook and new ways of handling quantum-mechanical problems, and also leads to improved approximation techniques for dealing with potentials of interest in all branches of physics. The algebraic approach to obtaining eigenstates is elegant and important, and all physicists should become familiar with this. The book has been written in such a way that it can be easily appreciated by students in advanced undergraduate quantum mechanics courses. Problems have been given at the end of each chapter, along with complete solutions to all the problems. The text also includes material of interest in current research not usually discussed in traditional courses on quantum mechanics, such as the connection between exact solutions to classical soliton problems and isospectral quantum Hamiltonians, and the relation to the inverse scattering problem. Contents: The Schrödinger Equation in One Dimension; Factorization of a General Hamiltonian; Shape Invariance and Solvable Potentials; Charged Particles in External Fields and Supersymmetry; Isospectral Hamiltonians; New Periodic Potentials from Supersymmetry; Supersymmetric WKB Approximation; Perturbative Methods for Calculating Energy Spectra and Wave Functions; Appendices: Path Integrals and SUSY; Operator Transforms - New Solvable Potentials from Old; Logarithmic Perturbation Theory; Solutions to Problems. Readership: Graduate and advanced undergraduate students and researchers in quantum, mathematical, theoretical and high energy physics.
Notlar:
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2017. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
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