Russian Physics Journal

, Volume 41, Issue 2, pp 129–136 | Cite as

Holomorphic representation of coherent states of a singular oscillator and their Darboux representation

  • V. G. Bagrov
  • B. F. Samsonov
Elementary Particle Physics And Field Theory


We consider the coherent states of a singular oscillator; these states are defined to be the characteristic states of an operator that reduces the number of basis functions for a discrete spectrum to one. We use the Darboux transform to study the coherent states of a transformed Hamiltonian. We obtain an expression for measures that can be used to decompose unity. We construct a holomorphic representation for the state vectors in the space of functions holomorphic everywhere in the complex plane, including vectors for discrete spectra and coherent states. We obtain a holomorphic representation of the Darboux transformation operators.


Coherent State Discrete Spectrum Moment Problem Modify Bessel Function Dynamic Symmetry 
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© Plenum Publishing Corporation 1998

Authors and Affiliations

  • V. G. Bagrov
  • B. F. Samsonov

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