  This paper presents a realistic model that describes radiation-matter
interactions. This is achieved by a generalization of first quantization, where
the Maxwell equations are interpreted as the electromagnetic component of the
Schroedinger equation. This picture is complemented by the consideration of
electrons and photons as real particles in three-dimensional space, following
guiding conditions derived from the particle-wave-functions to which they are
associated. The guiding condition for the electron is taken from Bohmian
mechanics, while the photon velocity is defined as the ratio between the
Poynting vector and the electromagnetic energy density. The case of many
particles is considered, taking into account their statistical properties. The
formalism is applied to a two level system, providing a satisfactory
description for spontaneous emission, Lamb shift, scattering, absorption,
dispersion, resonance fluorescence and vacuum fields. This model adequately
describes quantum jumps by the entanglement between the photon and the atomic
system and it will prove to be very useful in the simulation of quantum devices
for quantum computers and quantum information systems. A possible relativistic
generalization is presented, together with its relationship to QED.
