Two Kinds of Iterative Solutions for Generalized Sombrero-shaped Potential in $N$-dimensional Space

TL;DR

This paper develops two iterative methods to accurately compute ground state wave functions and energies for N-dimensional generalized Sombrero-shaped potentials, demonstrating convergence and consistency across different trial functions.

Contribution

It introduces and compares two novel iterative procedures for solving N-dimensional generalized Sombrero-shaped potentials, enhancing computational approaches in quantum mechanics.

Findings

Iterative solutions converge reliably to consistent results.

Different trial functions yield similar convergent solutions.

The methods are effective for N-dimensional potentials.

Abstract

Based on two different iteration procedures the groundstate wave functions and energies for N-dimensional generalized Sombrero-shaped potentials are solved. Two kinds of trial functions for the iteration procedure are defined. The iterative solutions are convergent nicely to consistent results for different choices of iteration procedures and trial functions.