Green's Function of a General PT-Symmetric Non-Hermitian Non-central Potential

TL;DR

This paper derives the Green's function for a class of PT-symmetric non-Hermitian non-central potentials by mapping the problem to two 2D harmonic oscillators, demonstrating the system's spectrum remains real and in unbroken PT phase.

Contribution

It provides an explicit Green's function solution for a general PT-symmetric non-Hermitian non-central potential, extending the understanding of such systems.

Findings

Green's functions expressed in terms of 2D harmonic oscillators

Spectrum remains real, indicating unbroken PT symmetry

Method applicable to a broad class of non-central potentials

Abstract

We study the path integral solution of a system of particle moving in certain class of PT symmetric non-Hermitian and non-central potential. The Hamil- tonian of the system is converted to a separable Hamiltonian of Liouville type in parabolic coordinates and is further mapped into a Hamiltonian corresponding to two 2-dimensional simple harmonic oscillators (SHOs). Thus the explicit Green's functions for a general non-central PT symmetric non hermitian potential are cal- culated in terms of that of 2d SHOs. The entire spectrum for this three dimensional system is shown to be always real leading to the fact that the system remains in unbroken PT phase all the time.