Eur. Phys. J. D 7, 475-478 (1999)
https://doi.org/10.1007/s100530050374

An asymptotic series solution to the Schrödinger equation for a model potential

¹ Department of Physics, National Taiwan University, Taipei 10764, Taiwan ROC
² Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 10764, Taiwan ROC
³ Department of Chemistry and Biochemistry, Arizona State University, Tempe, AZ 85287-1604, USA

Received: 8 June 1999
Published online: 15 December 1999

Abstract

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 four term recurrence 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.