This theory develops a quantum analog of the classical electron oscillator model. It argues first that the Hamiltonian of long-wave excitations of matter is equivalent to that of an assembly of oscillators under very general assumptions. Next, these oscillators are coupled with the electromagnetic field oscillators and the normal modes of the coupled system are analyzed. The normal modes of longitudinal and transverse excitation have different spectra; the transverse frequencies depend strongly on the wavelength but the longitudinal ones do not. If the "longitudinal photons" are eliminated after the transformation to normal modes, the resulting Coulomb law has the dielectric constant in the denominator. The dielectric response law is expressed as a series of oscillations and also in terms of Van Hove's correlation function. Born-approximation theory of the collisions of fast charged particles with the assembly of normal mode (longitudinal and transverse) oscillators yields the same total cross section as Fermi's macroscopic theory. The transverse excitations include the Čerenkov radiation.

• Received 8 May 1956

DOI:https://doi.org/10.1103/PhysRev.103.1202