Quantum mechanics is the underlying basic theory of matter for the mainstream models of physics. All other theoretical models can be proven mathematically to emerge from this quantum level . The basic tenet of quantum mechanics is that all observations and measurements depend on the probability of an interaction happening given by the wavefunction describing the system. A simple example is the hydrogen atom where the (x,y,z,t) of the electron around the proton is given by the wavefunction of the solution of the quantum mechanical equation for the hydrogen atom.. This means that to get the location of the electron around the proton one has to do many measurements and plot the distribution of the probability to find the electron. For complicated atoms and molecules one gets orbitals, not orbits. In the case of matter in bulk in addition the potentials entering by the attractive forces between molecules create lattices , and again their behavior is probabilistic.
A conductor is a system that has been modeled with quantum mechanics, and in the quantum mechanics of solids the electrons are not free, they are in various bound states. This link describes the quantum mechanical model of the band theory of solids:
Individual electrons are either in the conduction band or in the valence band. In the valence band the electrons are in energy levels of atoms and molecules. The energy levels in the conduction band are occupied by electrons that are bound to the whole lattice of the conductor, but still they are bound . This means that in order to leave the solid a photon of the correct energy and higher can kick them out of the quantum level (photoelectric).
Photons of lower energy but with the correct energy difference can change the energy level of the lattice bound electron, the low energy photon interacts with the whole lattice to do that. It is the same as with a photon raising the energy level of the electron in a simple atom.The conduction band though has so close energy levels of the lattice that the electrons can be modeled to be free within it, but the individual photon electron interaction goes through changes in the occupation of lattice energy levels.
You ask in the comments:
How does this translate to motion of the electron?
A single electron does not move. It just has a probability of being "found" in a given direction and position. It is the accumulation of electrons positions that can give the motion.
i still dont understand how change in the lattice energy level correlate to direction of the electron.
If one could solve the complicated potentials of a lattice when interacting with the photon, the wavefunction would have the probability of finding a single electron in the direction of the macroscopic current that emerges as the classical theory of electricity and magnetism.
In the simple atom example you gave, absorbed photon changes the electrons wave function so where it could be found. is something similar going on
yes, the quantum models are "averaging" keeping the quantum mechanical nature of the lattice of atoms and molecules.
