Bound states of the generalized spiked harmonic oscillator

TL;DR

This paper accurately computes bound states of the generalized spiked harmonic oscillator using the generalized pseudospectral method, providing new results across various potential parameters and states.

Contribution

It introduces an efficient numerical approach to calculate eigenvalues and densities for the generalized spiked harmonic oscillator, including excited states and a wide parameter range.

Findings

Accurate eigenvalues and densities for ground and excited states.

First-time reporting of many results for various potential parameters.

Analysis of potential parameters' effects on eigenvalues and densities.

Abstract

Bound states of the generalized spiked harmonic oscillator potential are calculated accurately by using the generalized pseudospectral method. Energy eigenvalues, various expectation values, radial densities are obtained through a nonuniform, optimal spatial discretization of the radial Schr\"odinger equation efficiently. Ground and excited states corresponding to arbitrary values of $n$ and $\ell$ are reported for potential parameters covering a wide range of interaction. Both weak and strong coupling is considered. The effect of potential parameters on eigenvalues and densities are discussed. Almost all of the results are reported here for the first time, which could be useful for future studies.