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Holomorphic representation of coherent states of a singular oscillator and their Darboux transformation. (English. Russian original) Zbl 0953.81032
Russ. Phys. J. 41, No. 2, 129-136 (1998); translation from Izv. Vyssh. Uchebn. Zaved., Fiz. 41, No. 2, 46-53 (1998).
Summary: We consider coherent states of a singular oscillator. These states are defined as the characteristic states of an operator that reduces by one the number of the basis function of the discrete spectrum. Using the technique of the Darboux transformation, we study the coherent states of the transformed Hamiltonian. We obtain an expression for the measure, which we use for decomposition of unity. We construct a holomorphic representation of the state vectors in the space of functions holomorphic in the entire complex plane, including the vectors of the discrete spectrum and the coherent states. We obtain a holomorphic representation of the operators of the Darboux transformation.

MSC:
81R30 Coherent states
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