  The exact spectrum of the Rabi hamiltonian is analytically found for
arbitrary coupling strength and detuning. I present a criterion for
integrability of quantum systems containing discrete degrees of freedom which
shows that in this case a finite symmetry group may entail integrability, even
without the presence of conserved charges beyond the hamiltonian itself.
Moreover, I introduce and solve a natural generalization of the Rabi model
which has no symmetries and is therefore probably the smallest non-integrable
physical system.
