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Generalized Rabi models: diagonalization in the spin subspace and differential operators of Dunkl type
A discrete parity symmetry of a two parameter extension of the
quantum Rabi model which smoothly interpolates between the latter and the
Jaynes-Cummings model, and of the two-photon and the two-mode quantum Rabi
models enables their diagonalization in the spin subspace. A more general
statement is that the respective sets of hermitian operators of the
Fulton-Gouterman type and those diagonal in the spin subspace are unitary
equivalent. The diagonalized representation makes it transparent that any
question about integrability and solvability can be addressed only at the level
of ordinary differential operators of Dunkl type. Braak's definition of
integrability is shown (i) to contradict earlier numerical studies and (ii) to
imply that any physically reasonable differential operator of Fulton-Gouterman
type is integrable.Comment: 6 pages, minor fine-tunin
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