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Ladder operators for isospectral oscillators

S. Seshadri·V. Balakrishnan·S. Lakshmibala
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Abstract

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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S. Seshadri, V. Balakrishnan, S. Lakshmibala. 1999-05-31. Ladder operators for isospectral oscillators. https://doi.org/10.1063/1.532355

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