Exact eigenvalues for the Coulomb potential with cut-off

✍ Scribed by Peter Linz; Tien Chi Chen

• Book ID: 104579059
• Publisher: John Wiley and Sons
• Year: 1977
• Tongue: English
• Weight: 425 KB
• Volume: 11
• Category: Article
• ISSN: 0020-7608
• DOI: 10.1002/qua.560110611

✦ Synopsis

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.