Form of the Hamiltonian and the initial conditions in radiation problems

The use of two of the most often employed forms of the Hamiltonian describing the interaction of atoms and molecules with an electromagnetic field is examined using the example of spontaneous emission. It is shown that formally the same initial state corresponds in the cases of different Hamiltonians to physically different initial conditions: a stationary Coulomb field exists in the initial state in one case and a nonstationary field, arising upon sudden excitation of the atom, exists in another. The differences in the initial conditions determine the differences in the photon spectra arising upon subsequent emission. The choice of initial conditions in real situations can be made by making a physical analysis of the excitation process. The Hamiltonian is transformed from one form to another. It is emphasized that the Hamiltonians are equivalent only if the states are correspondingly transformed. The Lamb-Retherford experiment is analyzed qualitatively.