  Quantum Rabi model has been exactly solved by employing the
parameter-dependent unitary transformation method in both the occupation number
representation and the Bargmann space. The analytical expressions for the
complete energy spectrum consisting of two double-fold degenerate sub-energy
spectra are presented in the whole range of all the physical parameters. Each
energy level is determined by a parameter in the unitary transformation, which
obeys a highly nonlinear equation. The corresponding eigenfunction is a
convergent infinite series in terms of the physical parameters. Due to the
level crossings between the neighboring eigenstates at certain physical
parameter values, such the degeneracies could lead to novel physical phenomena
in the two-level system with the light-matter interaction.
