The canonical form of the Rabi Hamiltonian

Journal Article · Fri Nov 01 00:00:00 EST 1996 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.531711· OSTI ID:388188

Szopa, M; Mys, G; Ceulemans, A ^[1]

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1. Department of Quantum Chemistry, University of Leuven, Celestijnenlaan 200F, B-3001 Leuven (Belgium)

The Rabi Hamiltonian, describing the coupling of a two-level system to a single quantized boson mode, is studied in the Bargmann{endash}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. {copyright} {ital 1996 American Institute of Physics.}

• OSTI ID: 388188
• Journal Information: Journal of Mathematical Physics, Vol. 37, Issue 11; Other Information: PBD: Nov 1996
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
HAMILTONIANS
SYMMETRY
HARMONIC OSCILLATORS
HILBERT SPACE
ANALYTIC FUNCTIONS
EIGENVALUES
FOCK REPRESENTATION
TWO-LEVEL SYSTEMS