The structure of supersymmetry in PT symmetric quantum mechanics

Abstract

The structure of supersymmetry is analyzed systematically in PT symmetric quantum mechanical theories. We give a detailed description of supersymmetric systems associated with one dimensional PT symmetric quantum mechanical theories. We show that there is a richer structure present in these theories compared to the conventional theories associated with Hermitian Hamiltonians. We bring out various properties associated with these supersymmetric systems and generalize such quantum mechanical theories to higher dimensions as well as to the case of one dimensional shape invariant potentials.

PT phase transition in higher-dimensional quantum systems

“…In fact the transformation in (2) is a rotation of an angle π in the x−y plane.This point is explained nicely by Bazeia et al [38]. The discrete parity transformation in two dimension therefore can be defined in two alternative ways,…”

Mathematical aspects of intertwining operators: the role of Riesz bases

“…Our conclusions are contained in section 4. It should be mentioned that the analysis of IO for non-self-adjoint operators was already considered, more on a physical side, in [14], and recently in [15]. In none of these papers, however, the role of Riesz bases was considered.…”

Reflectionless {\cal P}{\cal T} -symmetric potentials in the one-dimensional Dirac equation

“…A real k is a necessary condition for T Formulae (33)(34) immediately yield the corresponding coefficients for potential U 1 R…”

“…Note that P (x) plays the role of a superpotential. The fact that the supercharges (33) are not the Hermitian conjugates of each other gives rise to a richer structure of supersymmetric systems compared with Hermitian theories [33].…”