On the quasi - exact solvability of a singular potential in D - dimensions; confined and unconfined

Abstract

The D -dimensional quasi - exact solutions for the singular even - power anharmonic potential $V(q)=a{q}^2+b{q}^{-4}+c{q}^{-6}$ are reported. We show that whilst Dong and Ma's [5] quasi - exact ground - state solution (in D=2) is beyond doubt, their solution for the first excited state is exotic. Quasi - exact solutions for the ground and first excited states are also given for the above potential confined to an impenetrable cylindrical (D=2) or spherical (D=3) wall.

10 pages, no figures, Latex file, To appear in the Czech. J. Phys

References in corpus (2)

• Part of the D - dimensional Spiked harmonic oscillator spectra
• Anharmonic oscillators energies via artificial perturbation method