Extension of a Spectral Bounding Method to Complex Rotated Hamiltonians, with Application to $p^2-i{x}^3$

Abstract

We show that a recently developed method for generating bounds for the discrete energy states of the non-hermitian $-i{x}^3$ 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)).

Submitted to J. Phys. A

References in corpus (2)

• Generating Converging Bounds to the (Complex) Discrete States of the $P^2+i{X}^3+i\alpha X$ Hamiltonian
• Generating Converging Eigenenergy Bounds for the Discrete States of the -ix^3 Non-Hermitian Potential

Cited by in corpus (3)

• Generalized Householder Transformations for the Complex Symmetric Eigenvalue Problem
• Exact Christoffel-Darboux Expansions: A New, Multidimensional, Algebraic, Eigenenergy Bounding Method
• Comment on: `Numerical estimates of the spectrum for anharmonic PT symmetric potentials' [Phys. Scr. \textbf{85} (2012) 065005]