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 -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 nonlocal 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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February 1998
Research Article|
February 01 1998
Ladder operators for isospectral oscillators
S. Seshadri;
S. Seshadri
Department of Physics, Indian Institute of Technology, Madras 600 036, India
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V. Balakrishnan;
V. Balakrishnan
Department of Physics, Indian Institute of Technology, Madras 600 036, India
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S. Lakshmibala
S. Lakshmibala
Department of Physics, Indian Institute of Technology, Madras 600 036, India
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J. Math. Phys. 39, 838–847 (1998)
Article history
Received:
June 10 1997
Accepted:
October 09 1997
Citation
S. Seshadri, V. Balakrishnan, S. Lakshmibala; Ladder operators for isospectral oscillators. J. Math. Phys. 1 February 1998; 39 (2): 838–847. https://doi.org/10.1063/1.532355
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