Confinement in 3D polynomial oscillators through a generalized pseudospectral method

Abstract

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