Bound state spectra of the 3D rational potential

Abstract

We present bound state spectra of the 3D rational potential, $V(r)=r^2+\lambda r^2/(1+g{r}^2)$, $g>0$, by means of the generalized pseudospectral method. All the thirty states corresponding to $n$=0--9 are considered for the first time for a broad range of coupling parameters. These results surpass the accuracy of \emph{all} other existing calculations published so far except the finite-difference method, which yields similar accuracy as ours. Variation of energies and radial distribution functions is followed with respect to the interaction parameters. Special emphasis has been laid on \emph{higher} excitations and \emph{negative} values of the interaction, where relatively less work has been reported. The energy sequence is found to be different for positive and negative interaction; numerically following a mirror-image relationship \emph{usually}, if not always. Additionally, twenty energy splittings arising from certain levels belonging to $n$=0--9 are systematically studied as functions of the potential parameters. Several new states (including the higher ones) are presented.

15 pages, 5 tables, 2 figures, 55 references

References in corpus (8)

• Calculation of the spiked harmonic oscillators through a generalized pseudospectral method
• Spherically confined isotropic harmonic oscillator
• The generalized pseudospectral approach to the bound states of Hulthen and Yukawa potentials
• Calculation of the bound states of power-law and logarithmic potentials through a generalized pseudospectral method
• Studies on some singular potentials in quantum mechanics
• Studies on the hollow states of atomic lithium by a density functional approach
• Study of a class of non-polynomial oscillator potentials
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Cited by in corpus (8)

• Studies on bound-state spectra of Manning-Rosen potential
• Confinement in 3D polynomial oscillators through a generalized pseudospectral method
• Hybrid quantum-classical dynamics of pure-dephasing systems
• Studies on the bound-state spectrum of hyperbolic potential
• Information-Entropic Measures in Confined Isotropic Harmonic Oscillator
• Fisher information in confined isotropic harmonic oscillator
• A differentiation formula, with application to the two-dimensional Schrödinger equation
• Information analysis in free and confined harmonic oscillator