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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 1687-9120 1687-9139 |