A rigorous description of light–matter interaction requires a fully quantized system of field equations,
which is the content of quantum optics [70Hak, 95Wal, 97Scu, 95Man, 01Vog]. This theory
is well developed and the results are confirmed perfectly by many experiments (see Chap. 5.1).
But most problems of laser design and laser technology can be solved in a satisfactory way by
applying the semiclassical theory. This means a non-relativistic quantum-mechanical approach for
the electronic system and a non-quantized, classical electromagnetic field.
Non-relativistic means that the velocity of the interacting electrons is small compared with the
velocity of light. This holds for the outer shell electrons of the atoms and molecules, which are
relevant in laser physics. It is not true for the free-electron laser and for the interaction of strong
fields with plasmas, which demand a relativistic treatment.