Pseudo-Hermitian and PT -symmetric quantum systems with energy-dependent potentials: Bound-state solutions and energy spectra

Abstract

We introduce generalized versions of complex Scarf and Morse-type potentials that con- tain energy-dependent parameters. PT -symmetry and pseudo-hermiticity of the associated quantum systems are discussed, and a modified orthogonality relation and pseudo-norm are constructed. We show that despite energy-dependence, our systems can admit real energy spectra and normalizable solutions of bound-state type.

18 pages

References in corpus (4)

• Making Sense of Non-Hermitian Hamiltonians
• $\mathcal{P}\mathcal{T}$ symmetry breaking in waveguide arrays with competing loss/gain pairs
• Pseudo-Hermitian random matrix theory
• Pseudo Hermitian interactions in the Dirac Equation