The Canonical Form of the Rabi Hamiltonian
  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. 
Marek Szopa (University of Silesia, Katowice, Poland), Geert Mys and   Arnout Ceulemans (University of Leuven, Leuven, Belgium)