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 (6)

• Supersymmetry and Quantum Mechanics
• New exact treatment of the perturbed Coulomb interactions
• Exact Eigenvalues and Eigenfunctions of the Hulthen Potential in the PT-Symmetry for Any Angular Momentum
• Bound states of a more general exponential screened Coulomb potential
• A perturbative treatment for the bound states of the Hellmann potential
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