Mukunda, N. ; Sudarshan, E. C. G. ; Sharma, J. K. ; Mehta, C. L. (1980) Representations and properties of para-Bose oscillator operators. I. Energy position and momentum eigenstates Journal of Mathematical Physics, 21 (9). pp. 2386-2394. ISSN 0022-2488
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Official URL: http://link.aip.org/link/?JMAPAQ/21/2386/1E
Related URL: http://dx.doi.org/10.1063/1.524695
Abstract
Para-Bose commutation relations are related to the SL(2,R) Lie algebra. The irreducible representation Dα of the para-Bose system is obtained as the direct sum Dβ⊕Dβ+½ of the representations of the SL(2,R) Lie algebra. The position and momentum eigenstates are then obtained in this representation Dα, using the matrix mechanical method. The orthogonality, completeness, and the overlap of these eigenstates are derived. The momentum eigenstates are also derived using the wave mechanical method by specifying the domain of the definition of the momentum operator in addition to giving it a formal differential expression. By a careful consideration in this manner we find that the two apparently different solutions obtained by Ohnuki and Kamefuchi in this context are actually unitarily equivalent.
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to American Institute of Physics. |
| Keywords: | Hamiltonians; Quantum Mechanics; Two-dimensional Calculations; Three-dimensional Calculations; Molecules; Dipoles |
| ID Code: | 19611 |
| Deposited On: | 22 Nov 2010 12:18 |
| Last Modified: | 06 Jun 2011 11:32 |
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