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Journal of Mathematical Physics / Volume 54 / Issue 3 / ARTICLES / Quantum Mechanics

J. Math. Phys. 54, 032103 (2013); http://dx.doi.org/10.1063/1.4795137 (21 pages)

About a new family of coherent states for some SU(1,1) central field potentials

Dusan Popov1, Vjekoslav Sajfert2, Nicolina Pop1, and Viorel Chiritoiu1

1Department of Physical Foundations of Engineering, “Politehnica” University of Timişoara, Bv. Vasile Parvan No. 2, RO-300223 Timişoara, Romania
2Technical Faculty “M. Pupin” Zrenjanin, University of Novi Sad, Djure Djakovica bb, 23000 Serbia

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(Received 19 September 2011; accepted 13 February 2013; published online 19 March 2013)

In this paper, we shall define a new family of coherent states which we shall call the “mother coherent states,” bearing in mind the fact that these states are independent from any parameter (the Bargmann index, the rotational quantum number J, and so on). So, these coherent states are defined on the whole Hilbert space of the Fock basis vectors. The defined coherent states are of the Barut-Girardello kind, i.e., they are the eigenstates of the lowering operator. For these coherent states we shall calculate the expectation values of different quantum observables, the corresponding Mandel parameter, the Husimi's distribution function and also the P- function. Finally, we shall particularize the obtained results for the three-dimensional harmonic and pseudoharmonic oscillators.

© 2013 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. DENSITY MATRIX APPROACH OF THE SU(1,1) CENTRAL FIELD POTENTIALS
  3. THE “MOTHER COHERENT STATES”
  4. STATISTICAL PROPERTIES
  5. THERMAL STATES
  6. SOME PARTICULAR POTENTIALS
    1. The three dimensional isotropic harmonic oscillator potential
    2. The pseudoharmonic oscillator potential
  7. CONCLUDING REMARKS

KEYWORDS and PACS

Keywords

eigenvalues and eigenfunctions, harmonic oscillators, Hilbert spaces, quantum theory, vectors

PACS

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.4795137

PUBLICATION DATA

ISSN

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

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

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    References

    J. R. Klauder, K. A. Penson, and J.-M. Sixdeniers, “Constructing coherent states through solutions of Stieltjes and Hausdorff moment problems,” Phys. Rev. A 64(1), 013817 (2001).

    J.-P. Antoine, J.-P. Gazeau, P. Monceau, J. R. Klauder, and K. A. Penson, “Temporally stable coherent states for infinite well and Pöschl–Teller potentials,” J. Math. Phys. 42, 2349 (2001)JMAPAQ000042000006002349000001.



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