Some Mathematical Considerations on Solid State Physics in the Framework of the Phase Space Formulation of Quantum Mechanics

We propose, for a finite crystal, that the entire system be expressed in terms of the phase space, including momentum, configuration position and spin. This is to be done both classically and quantum mechanically. We illustrate this with a silicon crystal. Then, quantum mechanically measuring with a wire containing electrons, we obtain a theoretically good approximation for an electron in one semiconductor. As well, we outline what has to be done for any crystal.