Concluding Remarks and Overview

Abstract

In the last fifteen years supersymmetric quantum mechanics has increasingly been utilized as an elegant and effective method in various branches of theoretical physics. In the present book we have discussed some of the recent developments in supersymmetric quantum mechanics. Only a small number of applications in quantum and statistical physics have been treated. In Table 9.1 we give a list¹ of apphcations in quantum mechanics, mathematical, statistical, condensed-matter, atomic, and nuclear physics. It appears that the Witten model, which we have extensively studied, is the prototype of a supersymmetric model in quantum mechanics. Despite the fact that this model is rather simple, it finds applications, for example, in the study of classical stochastic dynamical systems. Even for the understanding of semiconductor heterojunctions the Witten model can be utilized. A detailed analysis of its classical and quasi-classical properties has revealed many interesting results. The most impressive one is the quasi-classical supersymmetric quantization condition derived and discussed in Chap. 6. This approximation leads to exact bound-state spectra of all (via the factorization method) completely solvable problems. In this respect, it is superior to the well-estabhshed WKB approx-imation.