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Journal of Mathematical Physics / Volume 22 / Issue 1

J. Math. Phys. 22, 78 (1981); http://dx.doi.org/10.1063/1.524756 (13 pages)

Representation and properties of para‐Bose oscillator operators. II. Coherent states and the minimum uncertainty states

J. K. Sharma1, C. L. Mehta1, N. Mukunda2, and E. C. G. Sudarshan2

1Physics Department, Indian Institute of Technology, New Delhi, 110029, India
2Centre for Theoretical Studies, Indian Institute of Science, Bangalore, 560012, India

The energy, position, and momentum eigenstates of a para‐Bose oscillator system were considered in paper I. Here we consider the Bargmann or the analytic function description of the para‐Bose system. This brings in, in a natural way, the coherent states ‖z;α〉 defined as the eigenstates of the annihilation operator ?. The transformation functions relating this description to the energy, position, and momentum eigenstates are explicitly obtained. Possible resolution of the identity operator using coherent states is examined. A particular resolution contains two integrals, one containing the diagonal basis ‖z;α〉〈z;α‖ and the other containing the pseudodiagonal basis ‖z;α〉〈−z;α‖. We briefly consider the normal and antinormal ordering of the operators and their diagonal and discrete diagonal coherent state approximations. The problem of constructing states with a minimum value of the product of the position and momentum uncertainties and the possible α dependence of this minimum value is considered.

KEYWORDS and PACS

Keywords

EIGENSTATES, ANNIHILATION OPERATORS, SL GROUPS, HILBERT SPACE, QUANTUM MECHANICS, POSITION OPERATORS

PACS

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.524756

PUBLICATION DATA

ISSN

0022-2488 (print)  
1089-7658 (online)

For access to fully linked references, you need to log in.
    N. Mukunda, E. C. G. Sudershan, J. K. Sharma, and C. L. Mehta, J. Math. Phys. 21, 2386 (1980JMAPAQ000021000009002386000001).

    J. K. Sharma, C. L. Mehta, and E. C. G. Sudarshan, J. Math. Phys. 19, 2089 (1978JMAPAQ000019000010002089000001).

    P. A. M. Dirac, Rev. Mod. Phys. 17, 195 (1945).


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