nt - p h / 99 05 10 0 v 1 3 1 M ay 1 99 9 Ladder operators for isospectral oscillators
نویسندگان
چکیده
We present, for the isospectral family of oscillator Hamiltonians, a systematic procedure for constructing raising and lowering operators satisfying any prescribed 'distorted' Heisenberg algebra (including the q-generalization). This is done by means of an operator transformation implemented by a shift operator. The latter is obtained by solving an appropriate partial isometry condition in the Hilbert space. Formal representations of the non-local operators concerned are given in terms of pseudo-differential operators. Using the new annihilation operators, new classes of coherent states are constructed for isospectral oscillator Hamiltonians. The corresponding Fock-Bargmann representations are also considered, with specific reference to the order of the entire function family in each case.
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