Abstract

An approximate recipe to the energy eigenvalues for the problem of non-relativistic hydrogen-like atom confined in a spherical cavity of impenetrable wall is presented. The method is based on proposing an ansatz solution with a cut-off function. The asymptotic behavior of the reduced Schrödinger equation is then considered for large r and small r . Some approximations are applied to deform some terms of the equation, which then allowed us to apply the Nikiforov-Uvarov method in both regions. A potential parameter δ is introduced that plays a crucial role in the calculations. In both cases, we obtained an algebraic equation for the energy, which then can be solved for the specific potential parameters.

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