Explicit solutions of Laplace equations with inverse square and and singular P\"oschl-Teller Potentials

TL;DR

This paper provides explicit analytical solutions to Dirichlet problems involving Laplace equations with inverse square and singular P"oschl-Teller potentials, enhancing understanding of these complex potential problems.

Contribution

It introduces closed-form solutions for Laplace equations with specific singular potentials, which were previously unresolved or only approximated.

Findings

Closed-form solutions for inverse square potential problems.

Analytical solutions for singular P"oschl-Teller potential cases.

Improved mathematical understanding of potential-influenced Laplace equations.

Abstract

In this article we give in analytical closed form the solutions of the Direchlet problems for the Laplace equations with inverse square and singular P\"oschl-Teller potentials