 Beginning with the Jaynes–Cummings Hamiltonian under coherent drive

where formula_22 is the lowering operator for the cavity field, and formula_23 is the atomic lowering operator written as a combination of Pauli matrices.The time dependence can be removed by transforming the wavefunction according to formula_24, leading to a transformed Hamiltonian

where formula_26.As it stands now, the Hamiltonian has four terms.