An alternative simple solution of the sextic anharmonic oscillator and perturbed Coulomb problems
Sameer M. Ikhdair
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 appearing in the wave equation satisfy certain constraints.
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