The Canonical Form of the Rabi Hamiltonian

Details The Canonical Form of the Rabi Hamiltonian The Canonical Form of the Rabi Hamiltonian

1996-06-29

arxiv.org/abs/quant-ph/9606035v1

J.Math.Phys. 37 (1996) 5402-5411

Physics

Quantum Physics

17 pages, LaTeX, no figures, to appear in J.Math.Phys

Scientific paper

10.1063/1.531711

The Rabi Hamiltonian, describing the coupling of a two-level system to a single quantized boson mode, is studied in the Bargmann-Fock representation. The corresponding system of differential equations is transformed into a canonical form in which all regular singularities between zero and infinity have been removed. The canonical or Birkhoff-transformed equations give rise to a two-dimensional eigenvalue problem, involving the energy and a transformational parameter which affects the coupling strength. The known isolated exact solutions of the Rabi Hamiltonian are found to correspond to the uncoupled form of the canonical system.

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