Darboux transformations of the Jaynes-Cummings Hamiltonian

Details Darboux transformations of the Jaynes-Cummings Hamiltonian Darboux transformations of the Jaynes-Cummings Hamiltonian

2004-01-16

arxiv.org/abs/quant-ph/0401092v1

J. Phys. A: Math. Gen. 37 (2004) 10115-10127

Physics

Quantum Physics

15 pages

Scientific paper

10.1088/0305-4470/37/43/007

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 Schr\"odinger 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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