Exact eigenvalues for the Coulomb potential with cut‐off

Abstract

The solution of the quantum‐mechanical one‐particle problem involving a Coulomb potential with a cut‐off contains Whittaker functions, difficult to evaluate individually. However, the energy expression involves a ratio of two contiguous Whittaker functions, and the entire ratio is easily expressed as a convergent continued fraction. Representative energy eigenvalues are calculated, correcting the errors due to an earlier Bessel function approximation by Wannier. Copyright © 1977 John Wiley & Sons, Inc.