The truncated Coulomb potential revisited

TL;DR

This paper revisits the truncated Coulomb potential by applying the Frobenius method to derive exact eigenfunctions and eigenvalues, enabling efficient spectrum analysis and interpolation of eigenvalues.

Contribution

It introduces a novel application of the Frobenius method with a recurrence relation to solve the Schrödinger equation for the truncated Coulomb potential, providing a new approach to spectrum analysis.

Findings

Exact eigenfunctions and eigenvalues obtained

Spectrum information derived from eigenvalue arrangement

Eigenvalues interpolated efficiently

Abstract

We apply the Frobenius method to the Schr\"{o}dinger equation with a truncated Coulomb potential. By means of the tree-term recurrence relation for the expansion coefficients we truncate the series and obtain exact eigenfunctions and eigenvalues. From a judicious arrangement of the exact eigenvalues we derive useful information about the whole spectrum of the problem and can obtain other eigenvalues by simple and straightforward interpolation.