Iterative Solution for Generalized Sombrero-shaped Potential in $N$-dimensional Space

TL;DR

This paper presents an explicit iterative method to solve for the ground state of the Schrödinger equation with a generalized sombrero-shaped potential in N-dimensional space, analyzing convergence and wave function dependence.

Contribution

It introduces a new convergent iterative approach for solving the Schrödinger equation with a generalized N-dimensional sombrero-shaped potential.

Findings

Convergence conditions for the iterative method are established.

The shape of the ground state wave function depends on potential parameters.

The method provides explicit solutions for the lowest energy state.

Abstract

An explicit convergent iterative solution for the lowest energy state of the Schroedinger equation with generalized $N$-dimensional Sombrero-shaped potential is presented. The condition for the convergence of the iteration procedure and the dependence of the shape of the groundstate wave function on the parameters are discussed.