An asymptotic series solution to the Schrödinger equation for a model potential
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Using the method of Frobenius, the attempt to find a closed-form solution to the Schrödinger equation for a model potential \(\) is described. Inspection of the series solution in the asymptotic region suggests a substitution of a fourtermrecurrence relation by a two term relation in order to extract explicit solutions that approach to those obtained for the hydrogen atom as \(\) smoothly. The resulting approximate solutions are compared with numerical ones and shown to provide a good basis set for high Rydberg states.
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