Non-Hermitian Hamiltonian versus E=0 localized states

TL;DR

This paper investigates zero energy localized states in a 2D system with a non-Hermitian, complex potential, analyzing how the imaginary component influences state localization both analytically and schematically.

Contribution

It introduces a method to construct localized states using coherent states in non-Hermitian systems with complex potentials, highlighting the effects of the imaginary part.

Findings

Imaginary potential component affects localization properties.

Analytical and schematic analysis of zero energy states.

Construction of localized states via coherent states.

Abstract

We analyze the zero energy solutions, of a two dimensional system which undergoes a non-radial symmetric, complex potential V(r,$\phi$). By virtue of the coherent states concept, the localized states are constructed, and the consequences of the imaginary part of the potential are found both analytically and schematically.