Introduction

Supersymmetry (SUSY) arose as a response to attempts by physicists to obtain a unified description of all basic interactions of nature. SUSY relates bosonic and fermionic degrees of freedom combining them into superfields which provides a more elegant description of nature. The algebra involved in SUSY is a graded Lie algebra which closes under a combination of commutation and anti-commutation relations. It may be noted here that so far there has been no experimental evidence of SUSY being realized in nature. Nevertheless, in the last fifteen years, the ideas of SUSY have stimulated new approaches to other branches of physics like atomic, molecular, nuclear, statistical and condensed matter physics as well as nonrelativistic quantum mechanics. Naively, unbroken SUSY leads to a degeneracy between the spectra of the fermions and bosons in a unified theory. Since this is not observed in nature one needs SUSY to be spontaneously broken. It was in the context of trying to understand the breakdown of SUSY in field theory that the whole subject of SUSY quantum mechanics was first studied…