Wide Effectiveness of a Sine Basis for Quantum-Mechanical Problems in d Dimensions
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. Wha...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2013/258203 |
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| author | Richard L. Hall Alexandra Lemus Rodríguez |
| author_facet | Richard L. Hall Alexandra Lemus Rodríguez |
| author_sort | Richard L. Hall |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-f4e634430e494aaf888779d21a3424a5 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-f4e634430e494aaf888779d21a3424a52025-02-03T01:04:04ZengWileyAdvances in Mathematical Physics1687-91201687-91392013-01-01201310.1155/2013/258203258203Wide Effectiveness of a Sine Basis for Quantum-Mechanical Problems in d DimensionsRichard L. Hall0Alexandra Lemus Rodríguez1Department of Mathematics and Statistics, Concordia University, 1455 de Maisonneuve Boulevard West, Montreal, QC, H3G 1M8, CanadaDepartment of Mathematics and Statistics, Concordia University, 1455 de Maisonneuve Boulevard West, Montreal, QC, H3G 1M8, CanadaIt 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.http://dx.doi.org/10.1155/2013/258203 |
| spellingShingle | Richard L. Hall Alexandra Lemus Rodríguez Wide Effectiveness of a Sine Basis for Quantum-Mechanical Problems in d Dimensions Advances in Mathematical Physics |
| title | Wide Effectiveness of a Sine Basis for Quantum-Mechanical Problems in d Dimensions |
| title_full | Wide Effectiveness of a Sine Basis for Quantum-Mechanical Problems in d Dimensions |
| title_fullStr | Wide Effectiveness of a Sine Basis for Quantum-Mechanical Problems in d Dimensions |
| title_full_unstemmed | Wide Effectiveness of a Sine Basis for Quantum-Mechanical Problems in d Dimensions |
| title_short | Wide Effectiveness of a Sine Basis for Quantum-Mechanical Problems in d Dimensions |
| title_sort | wide effectiveness of a sine basis for quantum mechanical problems in d dimensions |
| url | http://dx.doi.org/10.1155/2013/258203 |
| work_keys_str_mv | AT richardlhall wideeffectivenessofasinebasisforquantummechanicalproblemsinddimensions AT alexandralemusrodriguez wideeffectivenessofasinebasisforquantummechanicalproblemsinddimensions |