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

Sameer M. Ikhdair
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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.

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Sameer M. Ikhdair. 2007-02-26. An alternative simple solution of the sextic anharmonic oscillator and perturbed Coulomb problems. https://doi.org/10.1142/s0129183107011583

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