Susy for non-Hermitian Hamiltonians, with a view to coherent states

TL;DR

This paper extends supersymmetric quantum mechanics to non-Hermitian Hamiltonians using dual superpotentials, constructs bi-coherent states, and applies the framework to finance and other examples.

Contribution

It introduces a novel SUSY approach for non-Hermitian systems with dual superpotentials and analyzes bi-coherent states, expanding SUSY methods beyond Hermitian operators.

Findings

Bi-coherent states exhibit unique properties in non-Hermitian systems.

Application to Black-Scholes equation demonstrates practical relevance.

Extended SUSY framework broadens analysis tools for non-Hermitian quantum systems.

Abstract

We propose an extended version of supersymmetric quantum mechanics which can be useful if the Hamiltonian of the physical system under investigation is not Hermitian. The method is based on the use of two, in general different, superpotentials. Bi-coherent states of the Gazeau-Klauder type are constructed and their properties are analyzed. Some examples are also discussed, including an application to the Black-Scholes equation, one of the most important equations in Finance.