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

Format:

Book

Author/Creator:

Cooper, Fred, 1944-

Contributor:

Khare, Avinash.

Sukhatme, Uday Pandurang.

Language:

English

Subjects (All):

Supersymmetry.

Quantum theory.

Physical Description:

1 online resource (223 p.)

Edition:

1st ed.

Place of Publication:

Singapore ; River Edge, N.J. : World Scientific, c2001.

Language Note:

English

Summary:

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:

ch. 1. Introduction

ch. 2. The Schrödinger 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

ch. 3. Factorization of a general Hamiltonian. 3.1. Broken supersymmetry. 3.2. SUSY harmonic oscillator. 3.3. Factorization and the hierarchy of Hamiltonian

ch. 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. 4.3. Shape invariance and noncentral solvable potentials

ch. 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

ch. 6. Isospectral Hamiltonians. 6.1. One parameter family of isospectral potentials. 6.2. Generalization to [symbol]-parameter isospectral family. 6.3. Inverse scattering and solitons

ch. 7. New periodic potentials from supersymmetry. 7.1. Unbroken SUSY and the value of the Witten index. 7.2. Lamé potentials and their supersymmetric partners. 7.3. Associated Lamé potentials and their supersymmetric partners

ch. 8. Supersymmetric WKB approximation. 8.1. Lowest order WKB 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

ch. 9. Perturbative methods for calculating energy spectra and wave functions. 9.1. Variational approach. 9.2. SUSY [symbol] expansion method. 9.3. Supersymmetry and double well potentials. 9.4. Supersymmetry and the large-N expansion.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references and index.

ISBN:

9786611871567

9781281871565

1281871567

9789812386502

9812386505

OCLC:

646768482