Ladder operators for isospectral oscillators

Details Ladder operators for isospectral oscillators Ladder operators for isospectral oscillators

1999-05-31

arxiv.org/abs/quant-ph/9905100v1

J.Math.Phys. 39 (1998) 838-847

Physics

Quantum Physics

13 pages

Scientific paper

10.1063/1.532355

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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