Tavis-Cummings models and their quasi-exactly solvable Schrödinger Hamiltonians
Department of Physics, University of Guilan, 41635-1914, Rasht, Iran
2 Departamento de Fısica Teórica, Atómica y Óptica, IMUVA, Universidad de Valladolid, 47011, Valladolid, Spain
* e-mail: firstname.lastname@example.org
Accepted: 13 May 2019
Published online: 29 July 2019
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.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature, 2019