The good, the bad and the ugly coherent states through polynomial Heisenberg algebras

Miguel Castillo-Celeita () and David J. Fernández C. ()
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Miguel Castillo-Celeita: Cinvestav, Departamento de Física
David J. Fernández C.: Cinvestav, Departamento de Física

A chapter in Physical and Mathematical Aspects of Symmetries, 2017, pp 111-117 from Springer

Abstract: Abstract Second degree polynomial Heisenberg algebras are realized through the harmonic oscillator Hamiltonian, together with two deformed ladder operators chosen as the third powers of the standard annihilation and creation operators. The corresponding solutions to the Painlevé IV equation are easily found. Moreover, three different sets of eigenstates of the deformed annihilation operator are constructed, called the good, the bad and the ugly coherent states. Some physical properties of such states will be studied as well.

Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-69164-0_16

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DOI: 10.1007/978-3-319-69164-0_16

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