Representations and properties of para-Bose oscillator operators. I. Energy position and momentum eigenstates

Mukunda, N and Sudarshan, ECG and Sharma, JK and Mehta, CL (1980) Representations and properties of para-Bose oscillator operators. I. Energy position and momentum eigenstates. In: Journal of Mathematical Physics, 21 (9). pp. 2386-2394.

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Abstract

Para-Bose commutation relations are related to the SL(2,R) Lie algebra. The irreducible representation [script D]alpha of the para-Bose system is obtained as the direct sum Dbeta[direct-sum]Dbeta+1/2 of the representations of the SL(2,R) Lie algebra. The position and momentum eigenstates are then obtained in this representation [script D]alpha, 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. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

Item Type:	Journal Article
Publication:	Journal of Mathematical Physics
Publisher:	American Institute of Physics
Additional Information:	Copyright of this article belongs to American Institute of Physics.
Department/Centre:	Division of Physical & Mathematical Sciences > Physics
Date Deposited:	10 Feb 2010 10:49
Last Modified:	19 Sep 2010 05:35
URI:	http://eprints.iisc.ac.in/id/eprint/21097

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