Matrix superpotentials

Abstract

We present a collection of matrix valued shape invariant potentials which give rise to new exactly solvable problems of SUSY quantum mechanics. It includes all irreducible matrix superpotentials of the generic form W = kO + 1/kR + P where k is a variable parameter, Q is the unit matrix multiplied by a real valued function of independent variable x, and P, R are hermitianmatrices depending on x. In particular we recover the Pron'ko-Stroganov "matrix Coulomb potential" and all known scalar shape invariant potentials of SUSY quantum mechanics. In addition, five new shape invariant potentials are presented. © Springer Japan 2013.