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

## TL;DR

This paper explores complex energy-dependent quantum potentials, demonstrating that they can possess real spectra and bound states while maintaining PT-symmetry and pseudo-hermiticity, with implications for quantum system analysis.

## Contribution

It introduces generalized complex potentials with energy dependence, analyzes their symmetry properties, and constructs modified orthogonality relations and pseudo-norms.

## Key findings

- Energy-dependent potentials can have real spectra.
- Bound-state solutions are normalizable despite energy dependence.
- PT-symmetry and pseudo-hermiticity are preserved in these systems.

## 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.