Regularized Green's Function for the Inverse Square Potential

TL;DR

This paper develops a Green's function method for the quantum inverse square potential using hyperspherical coordinates and regularization, providing a closed-form solution and demonstrating equivalence with path-integral approaches.

Contribution

It introduces a novel Green's function approach with regularization for the inverse square potential, connecting it to path-integral methods.

Findings

Closed-form radial energy Green's function derived

Regularization scheme implemented successfully

Equivalence with path-integral treatment established

Abstract

A Green's function approach is presented for the D-dimensional inverse square potential in quantum mechanics. This approach is implemented by the introduction of hyperspherical coordinates and the use of a real-space regulator in the regularized version of the model. The application of Sturm-Liouville theory yields a closed expression for the radial energy Green's function. Finally, the equivalence with a recent path-integral treatment of the same problem is explicitly shown.