Wide effectiveness of a sine basis for quantum-mechanical problems in d dimensions
Mathematical Physics
2013-02-15 v1 math.MP
Abstract
It is shown that the spanning set for L^2([0, 1]) provided by the eigenfunctions {sqrt{2} sin(n\pi x)}_{n=1}^{\infty} of the particle-in-a-box in quantum mechanics provide a very effective variational basis for more general problems. The basis is scaled to [a,b], where a and b are then used as variational parameters. What is perhaps a natural basis for quantum systems confined to a spherical box in R^d, turns out to be appropriate also for problems that are softly confined by U-shaped potentials, including those with strong singularities at r=0. Specific examples are discussed in detail, along with some bound N-boson systems
Keywords
Cite
@article{arxiv.1212.4516,
title = {Wide effectiveness of a sine basis for quantum-mechanical problems in d dimensions},
author = {Richard L. Hall and Alexandra Lemus Rodriguez},
journal= {arXiv preprint arXiv:1212.4516},
year = {2013}
}
Comments
12 pages, 3 figures