Calculation of the bound states of power-law and logarithmic potentials through a generalized pseudospectral method

TL;DR

This paper introduces a generalized pseudospectral method to accurately compute bound states of power-law and logarithmic potentials in quantum mechanics, outperforming existing methods and reporting new states.

Contribution

The paper presents a novel generalized pseudospectral approach for solving the Schrödinger equation with specific potentials, achieving higher accuracy and discovering new bound states.

Findings

Accurate eigenvalues and expectation values for various states.

Significantly improved results over previous calculations.

Identification of new bound states.

Abstract

Bound states of the power-law and logarithmic potentials are calculated using a generalized pseudospectral method. The solution of the single-particle Schr\"odinger equation in a nonuniform and optimal spatial discretization offers accurate eigenvalues, densities and expectation values. The calculations are carried out for states with arbitrary $n$ and $\ell$ quantum numbers. Comparisons are made with the available literature data and excellent agreement is observed. In all the cases, the present method yields considerably improved results over the other existing calculations. Some new states are reported.