Exact eigenvalues, eigenfunctions, matrix elements and phase-shifts for a particle of angular momentum l in a particular screened potential

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Abstract
The radial Schrödinger equation is solved for an effective potential that can be considered as a generalization of a potential suggested by Hylleraas and Risberg and by Hulthén. For the scattering problem the phase‐shifts are deduced. For the bound state problem the energy eigenvalues and the normalized eigenfunctions are derived. Closed‐form expressions for certain matrix elements are calculated, and for the particular case of expectation values a recurrence formula is derived. In an appendix Levinson’s theorem is discussed for the particular potential under consideration.

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