ABSTRACT
This chapter discusses a few general properties of operators. The effect of reflection of the wave at a potential step is very familiar in other situations in physics, such as the partial reflection and partial transmission of a light wave at a surface where the index of refraction changes abruptly. Also, a signal in a transmission line will be partially reflected from a junction where there is an impedance mismatch. The simplest picture of the ground state of a solid is that of bands filled from the lowest Bloch state on up, with two electrons in each state. In the first the electrons exactly fill to the top of a band, with the next band entirely empty; such a solid behaves as an insulator. In the second, the topmost band having occupied states is only partially filled; such a solid will conduct electricity.
