Supersymmetry in quantum mechanics (Q2713345)

This book makes available an organized description of supersymmetric quantum mechanics (SQM). The authors review the theoretical formulation of SQM and discuss how supersymmetry (SUSY) helps in finding exact and approximate solutions to quantum-mechanical problems. SUSY harmonic oscillator, Pauli equation, Dirac equation, Dirac equation with a Lorentz scalar potential in \(1+1\) dimensions, Dirac particle in a Coulomb field, Dirac particle in a magnetic field are considered. The connection between inverse scattering and isospectral potentials helps to construct multi-soliton solutions of the Korteweg-de Vries equation. It is shown that using the ideas of SUSY and shape invariance, enables one to solve a number of potential problems algebraically. NEWLINENEWLINENEWLINENew types of approximations are developed to solve quantum-mechanical problems by the existence of a superpotential, partner potential, hierarchy of isospectral Hamiltonians. The authors focus on four new approximation methods, the \({1\over N}\) expansion within SQM, \(\delta\) expansion for the superpotential, a SUSY inspired WKB approximation and a variational method which utilizes the hierarchy of Hamiltonians related by SUSY and factorization. The many figures and exercises with answers make this book particularly suitable for students in advanced undergraduate and beginning graduate quantum-mechanical courses.