PT-/non-PT-Symmetric and non-Hermitian Hellmann Potential: Approximate Bound and Scattering States with Any $\ell$-Values

TL;DR

This paper explores approximate solutions for bound and scattering states of the non-Hermitian Hellmann potential in quantum mechanics, providing new energy eigenvalues, wave functions, and phase shifts for various angular momenta.

Contribution

It presents novel approximate analytical solutions for bound and scattering states of the PT-/non-PT-symmetric Hellmann potential, including energy spectra and phase shifts for any angular momentum.

Findings

Derived exact energy eigenvalues and wave functions.

Compared numerical energy values with previous results.

Analyzed phase shifts for scattering states.

Abstract

We investigate the approximate bound state solutions of the Schr\"odinger equation for the PT-/non-PT-symmetric and non Hermitian Hellmann potential. Exact energy eigenvalues and corresponding normalized wave functions are obtained. Numerical values of energy eigenvalues for the bound states are compared with the ones obtained before. Scattering state solutions are also studied. Phase shifts of the potential are written in terms of the angular momentum quantum number $\ell$.