Theoretical and Mathematical Physics

, Volume 201, Issue 1, pp 1503–1513 | Cite as

Full Analytic Spectrum of Generalized Jaynes-Cummings Hamiltonians

  • A. J. AdanmitondeEmail author
  • G. Y. H. AvossevouEmail author


We develop an analytic formalism using basic quantum mechanics techniques to successfully solve the multiphoton Jaynes–Cummings and the generalized Dicke Hamiltonians. For this, we split the Hamiltonians of these models into two operators that have the properties of constants of motion for these systems. We then use some well-known operator properties to obtain complete analytic spectra for the considered models.


quantum mechanics Jaynes–Cummings Hamiltonian commuting operator constant of motion confluent hypergeometric function 


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The authors thank the referee for a thorough review and the relevant comments that have helped to improve the work.

Conflicts of interest. The authors declare no conflicts of interest.


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© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Institut de Mathématiques et de Sciences PhysiquesUniversité d’Abomey-CalaviPorto-NovoRépublique du Bénin

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