General even and odd coherent states as solutions of discrete Cauchy problems. (English) Zbl 1038.39001
Nikitin, A. G. (ed.) et al., Proceedings of the fourth international conference on symmetry in nonlinear mathematical physics, Kyïv, Ukraine, July 9–15, 2001. Part 2. Dedicated to the 200th anniversary of M. Ostrohrads’kyi. Kyïv: Institute of Mathematics of NAS of Ukraine (ISBN 966-02-2486-9). Proc. Inst. Math. Natl. Acad. Sci. Ukr., Math. Appl. 43(2), 746-750 (2002).
The authors study the Cauchy problem for a linear homogeneous difference equation. Explicit and exact solutions of this problem are constructed. To reach this goal the authors use the following subresults. The first one is the choice of the fundamental set of solutions used. The second one is the expression in the closed form the first row of the product of an arbitrary number of the noncommutating matrices. This approach is exploited to solve the eigenvalue problem of a special set of non-Hermitian operators. A new class of generalized even and odd coherent states of a quantum harmonic oscillator are defined.
For the entire collection see [Zbl 0989.00035].
For the entire collection see [Zbl 0989.00035].
Reviewer: N. M. Ivanova (Kyïv)
