Groundstate with Zero Eigenvalue for Generalized Sombrero-shaped Potential in $N$-dimensional Space

TL;DR

This paper introduces an iterative method to solve the Schrödinger equation, revealing that certain generalized Sombrero-shaped potentials in N-dimensional space have groundstates with zero eigenvalue, under specific parameter restrictions.

Contribution

It presents a novel iterative approach for analyzing groundstates of complex potentials in higher dimensions, specifically identifying zero eigenvalue solutions for generalized Sombrero-shaped potentials.

Findings

Groundstates with zero eigenvalue exist for certain generalized Sombrero-shaped potentials.

Parameter restrictions are necessary for the zero eigenvalue groundstates.

The method applies to N-dimensional space, broadening analysis scope.

Abstract

Based on an iterative method for solving the goundstate of Schroedinger equation, it is found that a kind of generalized Sombrero-shaped potentials in N-dimensional space has groundstates with zero eigenvalue. The restrictions on the parameters in the potential are discussed.