Effective Hamiltonians from first principles

The equations of motion for a quantum system of the electromagnetic field interacting with matter are derived from the first principle Hamiltonian (two-level atomic systems are assumed) and from the effective Hamiltonian. The derivation is based on the memoryfunction theory of Mori and on the theory of random frequency modulation of Tokuyama and Mori. On the ground of comparison of the equations of motion from the first principle Hamiltonian with those from the effective Hamiltonian a justification of the use of effective Hamiltonians is discussed.