Shows that coherent states as defined by Mikhailov, (see Teor. Mat. Fiz., no.15, p.367 of 1974) may be considered in certain special cases as intelligent states.
In the frame of our approach we constructed the generalized oscillator connected with Krawtchouk polynomials (named Krawtchouk oscillator) and coherent states for this oscillator too. Ours results are compared with analogues ones obtained for another variant of Krawtchouk oscillator in the paper [N.M.Atakishiev and S.K.Suslov, Difference analogs of the harmonic oscillator, Teor. Mat. Fiz., 85, 64-73 (1990)] from other point of view. Our definition of coherent states is close to one given in [B.Roy and P.Roy, Phase properties of a new nonlinear coherent state, quant-ph/0002043] This investigation is partially supported by RFBR grant No 06-01-00451
Various definitions of the coherent states of the angular momentum are shown to be special cases of the oscillator-like coherent states of the groups SU(2) and SO(3) obtained by Mikhailov on the basis of a generalized Schwinger boson realization of the angular momentum algebra. This realization is then generalized to that of the angular momentum algebra of an asymmetric top by means of a transformation from the Euler angles to the Cayley–Klein parameters. The oscillator-like coherent states of an asymmetric top, analogous to those of Mikhailov, are then constructed. It is, then, shown that Janssen's and Mostowski's definitions of the coherent states of a top are special cases of these.