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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
  • 21 Downloads

Abstract

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.

Keywords

Coherent State Discrete Spectrum Moment Problem Modify Bessel Function Dynamic Symmetry 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • V. G. Bagrov
  • B. F. Samsonov

There are no affiliations available

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