Some remarks on a model of supersymmetric quantum mechanics

Asao Arai

First it is shown in an abstract mathematical framework of supersymmetric quantum theory that, under some conditions for the perturbation, the wave and the scattering operators on bosonic states have some connections with those on fermionic ones. In particular, a unitary equivalence between the two scattering operators is proved. Then, a class of supersymmetric quantum mechanical models on Rn is discussed and the abstract general results are applied to obtain some more explicit results on the supersymmetric potential scattering.

A. D. Jannussis, I. Tsohantzis, D. Vavougios

M. Kibler, Mohammed Daoud A

Bhashyam Balaji

Supersymmetry (SUSY), or Bose-Fermi symmetry, is an attempt to provide a unified description of all of the fundamental interactions. Although originally introduced in the quantum field theory context, it was noted by Witten that the understanding of certain features of SUSY was simpler in the quantum mechanical setting. Some aspects of the vast subject of supersymmetric quantum mechanics, and the supersymmetric Fokker-Planck equation, of relavance to continuous-time nonlinear filtering theory are briefly reviewed. The applicability of certain remarkable results in supersymmetric quantum mechanics to nonlinear filtering is noted and illustrated with a few examples.

Anton Galajinsky, Ivan Masterov

Georg Junker, Stephan Matthiesen

We study the classical properties of a supersymmetric system which is often used as a model for supersymmetric quantum mechanics. It is found that the classical dynamics of the bosonic as well as the fermionic degrees of freedom is fully described by a so-called quasi-classical solution. We also comment on the importance of this quasi-classical solution in the semi-classical treatment of the supersymmetric quantum model.