**On the spectrum of the quantum Rabi model**

The quantum Rabi model is the simplest physical model of the interaction between radiation and matter which is a central problem in quantum optics ([1]). The Hamiltonian of this model is a

self-adjoint operator with discrete spectrum. We present its definition, basic properties and a rigorous statement concerning the procedure which is called GRWA (Generalized Rotating-Wave

Approximation) in the physical literature following [2]. We show how our result allows one to solve the corresponding inverse problem, i.e. to reconstruct all parameters of the model from the spectrum.

The talk is based on joint work with A. Boutet de Monvel.

- D. Braak, Q.-H. Chen, M. T. Batchelor, and E. Solano: Semi-classical and quantum Rabi models: in celebration of 80 years,
*J. Phys. A: Math. Theor*., 49 (2016), no. 30, 30030 - E. K. Irish: Generalized rotating-wave approximation for arbitrarily large coupling,
*Phys. Rev. Lett*. 99 (2007), 173601