{"paper":{"title":"Wide effectiveness of a sine basis for quantum-mechanical problems in d dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Alexandra Lemus Rodriguez, Richard L. Hall","submitted_at":"2012-12-18T21:44:41Z","abstract_excerpt":"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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.4516","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}