Extension of a Spectral Bounding Method to Complex Rotated Hamiltonians, with Application to $p^2-ix^3$

TL;DR

This paper extends a spectral bounding method to complex rotated Hamiltonians, enabling better analysis of resonant states and bound states in non-Hermitian quantum systems, exemplified by the $p^2 - ix^3$ potential.

Contribution

It adapts a spectral bounding technique to complex rotated Hamiltonians, broadening its applicability to non-Hermitian quantum problems.

Findings

Method successfully applied to complex rotated $-ix^3$ Hamiltonian

Enables analysis of resonant states and Regge poles

Provides bounds for discrete energy states in complex potentials

Abstract

We show that a recently developed method for generating bounds for the discrete energy states of the non-hermitian $-ix^3$ potential (Handy 2001) is applicable to complex rotated versions of the Hamiltonian. This has important implications for extension of the method in the analysis of resonant states, Regge poles, and general bound states in the complex plane (Bender and Boettcher (1998)).