Exact solution of inverse-square-root potential $V\left(r\right)=-\frac{\alpha }{\sqrt{r}}$

Abstract

An exact solution of the three-dimensional spherical symmetry inverse-square-root potential $V\left(r\right)=-\frac{\alpha }{\sqrt{r}}$, including scattering and bound-state solutions, is presented.

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• Scattering of a Klein-Gordon particle by a smooth barrier
• Study of superradiance in the Lambert-W potential barrier
• Perturbation-based Non-perturbative Method