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Tavis-Cummings models and their quasi-exactly solvable Schrödinger Hamiltonians

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Abstract.

We study in detail the relationship between the Tavis-Cummings Hamiltonian of quantum optics and a family of quasi-exactly solvable Schrödinger equations. The connection between them is established through the biconfluent Heun equation. We found that each invariant n-dimensional subspace of Tavis-Cummings Hamiltonian corresponds either to n potentials, each with one known solution, or to one potential with n known solutions. Among these Schrödinger potentials the quarkonium and the sextic oscillator appear.

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Authors and Affiliations

  1. Department of Physics, University of Guilan, 41635-1914, Rasht, Iran

    T. Mohamadian & H. Panahi

  2. Departamento de Fısica Teórica, Atómica y Óptica, IMUVA, Universidad de Valladolid, 47011, Valladolid, Spain

    J. Negro & L. M. Nieto

Authors
  1. T. Mohamadian
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  2. J. Negro
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  3. L. M. Nieto
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  4. H. Panahi
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Correspondence to J. Negro.

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Mohamadian, T., Negro, J., Nieto, L.M. et al. Tavis-Cummings models and their quasi-exactly solvable Schrödinger Hamiltonians. Eur. Phys. J. Plus 134, 363 (2019). https://doi.org/10.1140/epjp/i2019-12753-4

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