The power-law and the logarithmic potentials

TL;DR

This paper demonstrates an efficient variational method to compute energy eigenvalues and eigenfunctions for power-law and logarithmic potentials in the Schrödinger equation, achieving results that closely match exact numerical solutions.

Contribution

Introduces a variational approach with special wave functions for solving Schrödinger equations with specific potentials, simplifying calculations.

Findings

Results agree well with exact numerical solutions

Method provides a straightforward way to obtain eigenvalues and eigenfunctions

Applicable to power-law and logarithmic potentials

Abstract

In this study, we show that the energy eigenvalues and the eigenfunctions of the Schrodinger equation for the power-law and the logarithmic potential can be easily obtained by using variation technique for special type wave functions. The results are in very good agreement with exact numerical results.