Calculation of the spiked harmonic oscillators through a generalized pseudospectral method

TL;DR

This paper introduces a generalized pseudospectral method for accurately calculating eigenvalues and states of spiked harmonic oscillators, offering a simple, efficient approach for complex singular potentials in quantum mechanics.

Contribution

The paper presents a novel generalized pseudospectral method that enables precise and efficient computation of eigenvalues and states for spiked harmonic oscillators, including higher excited states.

Findings

Results agree well with existing methods

Accurately computes ground and excited states

Reports new higher excited states for the first time

Abstract

The generalized pseudospectral method is employed for the accurate calculation of eigenvalues, densities and expectation values for the spiked harmonic oscillators. This allows \emph{nonuniform} and \emph{optimal} spatial discretization of the corresponding single-particle radial Schr\"odinger equation satisfying the Dirichlet boundary conditions leading to the standard diagonalization of the symmetric matrices. The present results for a large range of potential parameters are in excellent agreement with those from the other accurate methods available in the literature. The ground and excited states (both low as well as high angular momentum states) are obtained with equal ease and accuracy. Some new states including the higher excited states are reported here for the first time. This offers a simple, accurate and efficient method for the treatment of these and a wide variety of other singular potentials of physical and chemical interest in quantum mechanics.