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

Richard L. Hall and Alexandra Lemus Rodríguez

Advances in Mathematical Physics, 2013, vol. 2013, issue 1

Abstract: It is shown that the spanning set for L2([0,1]) provided by the eigenfunctions {2sin (nπx)} n=1∞ of the particle in a box in quantum mechanics provides 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 Rd 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.

Date: 2013
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https://doi.org/10.1155/2013/258203

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2013:y:2013:i:1:n:258203

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