The canonical form of the Rabi Hamiltonian
- 1 November 1996
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 37 (11) , 5402-5411
- https://doi.org/10.1063/1.531711
Abstract
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.Comment: 17 pages, LaTeX, no figures, to appear in J.Math.PhyKeywords
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