Journal of Applied Mathematics
Volume 2 (2002), Issue 6, Pages 265-275

Explicit summation of the constituent WKB series and new approximate wave functions

Vladimir V. Kudryashov1 and Yulian V. Vanne2

1Institute of Physics, National Academy of Sciences of Belarus, 68 F. Skaryna Avenue, Minsk 220072, Belarus
2Department of Chemistry, University of Konstanz, Fach M721 D-78457, Konstanz, Germany

Received 6 December 2001; Revised 11 April 2002

Copyright © 2002 Vladimir V. Kudryashov and Yulian V. Vanne. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The independent solutions of the one-dimensional Schrödinger equation are approximated by means of the explicit summation of the leading constituent WKB series. The continuous matching of the particular solutions gives the uniformly valid analytical approximation to the wave functions. A detailed numerical verification of the proposed approximation is performed for some exactly solvable problems arising from different kinds of potentials.