Abstract
A semiclassical analog to the Abraham-Moses-Gel'fand-Levitan method for generating radial potentials with analytic sets of energy levels is presented. The algorithm begins with the selection of a model potential whose energy levels can be expressed as analytic functions of the corresponding quantum numbers. Then, a finite number of states is deleted from its spectrum, leaving all the others unchanged. Subsequently, the incomplete spectrum is analytically inverted using a generalized version of the Rydberg-Klein-Rees equations. The result is a family of potential functions that, when quantized, give rise to the incomplete spectra. Emphasis is placed on the application of this method to a Coulomb model potential. The simple l-dependent analytic functions obtained allow the straightforward calculation and systematic study of a number of members of this modified Coulomb-potential family. The connection between these modifications and atomic pseudopotentials is also discussed.
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