Novel Bound States Treatment of the Two Dimensional Schrodinger Equation with Pseudocentral Plus Multiparameter Noncentral Potential

TL;DR

This paper solves the two-dimensional Schrödinger equation with a pseudo central plus noncentral potential, deriving explicit bound state energies and wavefunctions using an analytical method, aiding quantum system analysis.

Contribution

It introduces a novel approach to solving the 2D Schrödinger equation with a combined potential, providing explicit solutions and extending previous results.

Findings

Exact bound state energy spectra obtained

Explicit wavefunctions derived in closed form

Results consistent with previous studies

Abstract

By converting the rectangular basis potential V(x,y) into the form as V(r)+V(r, phi) described by the pseudo central plus noncentral potential, particular solutions of the two dimensional Schrodinger equation in plane-polar coordinates have been carried out through the analytic approaching technique of the Nikiforov and Uvarov (NUT). Both the exact bound state energy spectra and the corresponding bound state wavefunctions of the complete system are determined explicitly and in closed forms. Our presented results are identical to those of the previous works and they may also be useful for investigation and analysis of structural characteristics in a variety of quantum systems