Diagonalizing the Jaynes-Cummings Hamiltonian and Jaynes-Cummings coherent states

We determine the form of the unitary transformation that diagonalizes the Jaynes-Cummings Hamiltonian. This leads to operators the action of which has a simple interpretation in terms of the dressed states, the energy eigenstates. This suggests a set of coherent states and spin coherent states based on the dressed states.