Bound states of the generalized spiked harmonic oscillator

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.