https://doi.org/10.1140/epjp/s13360-022-03323-0
Regular Article
Para-Bose oscillator algebras of odd orders: x-representations and Wigner functions for coherent and cat states and their photon-added and photon-subtracted counterparts
Department of Theoretical Physics and Astrophysics, Faculty of Physics, University of Tabriz, P. O. Box 51666-16471, Tabriz, Iran
Received:
26
July
2022
Accepted:
25
September
2022
Published online:
31
October
2022
The expansion coefficients for the Glauber-type coherent states 
of a para-Bose algebra of odd order 
are expressed in terms of the Laguerre polynomials of order 
in 
. It allows us to use one of the generating functions of the Laguerre polynomials to obtain the x-representation of the coherent states in terms of the J-Bessel functions. This, in turn, makes it possible to evaluate x-representations of the even and odd cat states as well as the m-photon-added and m-photon-subtracted coherent and cat states of the para-Bose oscillator algebra of odd order 
. Finally, with the help of these x-representations, we are able to examine Wigner functions and observe the non-classical behaviors via negative values for the probability distribution functions in phase space.
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