Fock-Bargman Representation of the Distorted Heisenberg Algebra

Abstract

The dynamical algebra associated to a family of Isospectral Oscillator Hamiltonians, named {\it Distorted Heisenberg Algebra} because its dependence on a distortion parameter $W\ge 0$, has been recently studied. The connection of this algebra with the Hilbert space of entire functions of growth (1/2, 2) is analized.

10 pages, Latex, 0 figures. Minor revisions and changes in the above version. A new number operator $N_w$ which dependence as a function of the Hamiltonian $H{}_{\lambda }$ has been discussed. Submitted to J. Phys. A: Math. Gen. 1996