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Darboux transformations of the Jaynes-Cummings Hamiltonian

Boris F Samsonov·Javier Negro
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Abstract

A detailed analysis of matrix Darboux transformations under the condition that the derivative of the superpotential be self-adjoint is given. As a onsequence, a class of the symmetries associated to Schrödinger matrix Hamiltonians is characterized. The applications are oriented towards the Jaynes-Cummings eigenvalue problem, so that exactly solvable $2\times 2$ matrix Hamiltonians of the Jaynes-Cummings type are obtained. It is also established that the Jaynes-Cummings Hamiltonian is a quadratic function of a Dirac-type Hamiltonian.

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Boris F Samsonov, Javier Negro. 2004-01-16. Darboux transformations of the Jaynes-Cummings Hamiltonian. https://doi.org/10.1088/0305-4470/37/43/007

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