Generating Converging Bounds to the (Complex) Discrete States of the $P^2 + iX^3 + i\alpha X$ Hamiltonian

Abstract

The Eigenvalue Moment Method (EMM), Handy (2001), Handy and Wang (2001)) is applied to the $H_\alpha \equiv P^2 + iX^3 + i\alpha X$ Hamiltonian, enabling the algebraic/numerical generation of converging bounds to the complex energies of the $L^2$ states, as argued (through asymptotic methods) by Delabaere and Trinh (J. Phys. A: Math. Gen. {\bf 33} 8771 (2000)).