Violeta Tretynyk
International Science and Technology University,
3 Magnitogorsky provulok, Kyiv (UKRAINA)
E-mail: violeta8505@altavista.com

Resolution of a general linear homogeneous recursive equation: an application to quantum optics

The detailed construction of a prefixed fundamental set of solutions of a linear homogeneous difference equation of any order and with arbitrarily variable coefficients is reported. The approach is quite general and relies on a novel and successful treatment of the linear recursion appropriately cast in matrix form. The usefulness of the resulting resolutive formula is illustrated widely discussing some physical and mathematical examples. In particular a simple application to the Hermite polynomials is presented. Moreover an interesting connection between a combinatorial problem and the generalized Fibonacci sequence is brought to the light. Finally the results are exploited to introduce generalized even and odd coherent states of a quantum harmonic oscillator. Some aspects of these nonclassical states are briefly put into evidence.