Fredholm Method for Podolsky Quantum Wave Function

TL;DR

This paper applies the Fredholm method to solve Schroedinger's integral equation for scattering problems involving Coulombian and Podolsky potentials, highlighting Podolsky's potential in regularizing wave function behavior near the scattering center.

Contribution

It introduces the use of Podolsky potential within the Fredholm method to address singularities in quantum scattering, offering a novel regularization approach.

Findings

Podolsky potential regularizes wave function near scattering center

Coulomb potential causes strong amplitude variation

Podolsky potential removes strong variation with a constant

Abstract

In this paper we used the Fredholm method in Schroedinger's integral equation in the investigation of the scattering effect near the center of it between a stationary quantum wave function and an electrostatic potential. Two potentials are studied one Coulombian and the other Podolsky. The result shows the importance of the proposal of Podolsky to regularize the effect near the scattering center in the quantum wave function. Being that the coulombian potential presents with strong variation in the amplitude of the wave after the scattering. In the case of Podolsky's potential, this is corrected by adopting a constant that removes this strong variation.