Barut-Girardello coherent states of the pseudoharmonic oscillator

In the paper we have investigated some properties off the Barut-Giraradello coherent states (BGCS) (the eigenstates of the SU(1, 1) lowering generator K_) for the Hamiltonian of the pseudoharmonic oscillator (PHO). By using t hese states, the diagonal P-representation of the density operator is const ructed as a new result for this potential. In addition, we have calculated some thermal expectation values for the quantum canonical gas of the PHOs. The calculations using the BGCS representation seem to be much simpler and easier to program than the corresponding calculations in other representati ons (e.g. the position representation). At the end of the paper the time de pendence of these states is presented.