LADDER OPERATORS FOR ISOSPECTRAL OSCILLATORS

We present, for the isospectral family of oscillator Hamiltonians, a s ystematic procedure for constructing raising and lowering operators sa tisfying any prescribed ''distorted'' Heisenberg algebra (including th e q-generalization). This is done by means of an operator transformati on implemented by a shift operator. The latter is obtained by solving an appropriate partial isometry condition in the Hilbert space. Formal representations of the nonlocal operators concerned are given in term s of pseudo-differential operators. Using the new annihilation operato rs, new classes of coherent states are constructed for isospectral osc illator Hamiltonians. The corresponding Fock-Bargmann representations are also considered, with specific reference to the order of the entir e function family in each case. (C) 1998 American Institute of Physics . [S0022-2488(98)03301-5].