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

T. Mohamadian, J. Negro, L. M. Nieto, H. Panahi

备注：: 14 pages, 6 figures
发表信息：: Eur. Phys. J. Plus 134, 363 (2019)

英文摘要：

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 stablished 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 appear the quarkonium and the sextic oscillator.

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