At operator level, the microscopic polarization is defined by an expectation value for a single electronic transition between a valence and a conduction band. In second quantization, conduction-band electrons are defined by fermionic creation and annihilation operators a ^ ^ c , k † † and a ^ ^ c , k , respectively. An analogous identification, i.e., a ^ ^ v , k † † and a ^ ^ v , k , is made for the valence band electrons. The corresponding electronic interband transition then becomes