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

Richard L. Hall and Alexandra Lemus Rodríguez

Advances in Mathematical Physics, 2013, vol. 2013, 1-10

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.

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlamp:258203

DOI: 10.1155/2013/258203

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