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Photon-added Barut-Girardello coherent states of the pseudoharmonic oscillator

Domenii publicaţii > Fizica + Tipuri publicaţii > Articol în revistã ştiinţificã

Autori: Dusan Popov

Editorial: Journal of Physics A: Mathematical and General, 35, p.7205 - 722, 2002.


In a previous paper (Popov D 2001 J. Phys. A: Math. Gen. 34 5283) we have
constructed the coherent states (CSs) of the pseudoharmonic oscillator (PHO).
These states are of the Barut-Girardello type. In the present paper, we have constructed and investigated some properties of the photon-added
Barut-Girardello coherent states (PA-BGCSs) of the PHO. These states are
not orthogonal but are normalized and satisfy a unity resolution relation
(the completeness relation). We have found the analytical form for the
positive weight function in the resolution of unity. By using these states, we have calculated some expectation values (the first two powers of the number operator N), which have evinced some non-classical properties. In order to examine the statistical properties of a PHO gas, which obeys the quantum canonical distribution, the diagonal P-representation of the density operator
is constructed and the thermal expectation values are calculated. All these quantities are expressed in terms of Meijer G-functions, and so the PA-BGCSs are a new field of application for these functions. Also, the time dependence of the PA-BGCSs is examined. If in the obtained results we put m = 0, we recover all the results from our previous paper.

Cuvinte cheie: coherent states, pseudoharmonic oscillator, density matrix, statistical properties, diagonal representation