An alternative simple solution of the sextic anharmonic oscillator and perturbed Coulomb problems

Abstract

Utilizing an appropriate ansatz to the wave function, we reproduce the exact bound-state solutions of the radial Schrodinger equation to various exactly solvable sextic anharmonic oscillator and confining perturbed Coulomb models in $D$-dimensions. We show that the perturbed Coulomb problem with eigenvalue $E$ can be transformed to a sextic anharmonic oscillator problem with eigenvalue E. We also check the explicit relevance of these two related problems in higher-space dimensions. It is shown that exact solutions of these potentials exist when their coupling parameters with $k=D+2\ell$ appearing in the wave equation satisfy certain constraints.

15 pages

References in corpus (3)

• Bound states of a more general exponential screened Coulomb potential
• A perturbative treatment for the bound states of the Hellmann potential
• Bound energy for the exponential-cosine-screened Coulomb potential

Cited by in corpus (2)

• Exact solutions of the modified Kratzer potential plus ring-shaped potential in the D-dimensional Schrodinger equation by the Nikiforov-Uvarov method
• Approximate l-state solutions of the D-dimensional Schrodinger equation for Manning-Rosen potential