Confinement in 3D polynomial oscillators through a generalized pseudospectral method

Abstract

Spherical confinement in 3D harmonic, quartic and other higher oscillators of even order is studied. The generalized pseudospectral method is employed for accurate solution of relevant Schrödinger equation in an \emph{optimum, non-uniform} radial grid. Eigenvalues, eigenfunctions, position expectation values, radial densities in \emph{low and high-lying} states are presented in case of \emph{small, intermediate and large} confinement radius. The \emph{degeneracy breaking} in confined situation as well as correlation in its \emph{energy ordering} with respect to the respective unconfined counterpart is discussed. For all instances, current results agree excellently with best available literature results. Many new states are reported here for first time. In essence, a simple, efficient method is provided for accurate solution of 3D polynomial potentials enclosed within spherical impenetrable walls.

17 pages, 5 figures, 6 tables

References in corpus (7)

• 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
• Study of a confined Hydrogen-like atom by the Asymptotic Iteration Method
• Calculation of the bound states of power-law and logarithmic potentials through a generalized pseudospectral method
• Supersymmetric variational energies of 3d confined potentials
• Bound state spectra of the 3D rational potential

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• Quantum confinement in 1D systems through an imaginary-time evolution method
• Fisher information in confined isotropic harmonic oscillator
• Information-Entropic Measures in Confined Isotropic Harmonic Oscillator