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Advances in Mathematical Physics
Volume 2013 (2013), Article ID 258203, 10 pages
http://dx.doi.org/10.1155/2013/258203
Research Article

Wide Effectiveness of a Sine Basis for Quantum-Mechanical Problems in Dimensions

Department of Mathematics and Statistics, Concordia University, 1455 de Maisonneuve Boulevard West, Montreal, QC, Canada H3G 1M8

Received 24 October 2012; Accepted 18 December 2012

Academic Editor: D. E. Pelinovsky

Copyright © 2013 Richard L. Hall and Alexandra Lemus Rodríguez. 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.

Abstract

It is shown that the spanning set for provided by the eigenfunctions of the particle in a box in quantum mechanics provides a very effective variational basis for more general problems. The basis is scaled to , where and are then used as variational parameters. What is perhaps a natural basis for quantum systems confined to a spherical box in turns out to be appropriate also for problems that are softly confined by U-shaped potentials, including those with strong singularities at . Specific examples are discussed in detail, along with some bound -boson systems.