ABSTRACT
We have commented several times, in the previous chapters, that each of our quantum states found in the various systems to which we have guided our attention, that each electron quantum state will actually hold two electrons. But these two electrons must have opposite spin. This is constituted by the particular constraints that are introduced by the fact that the electrons are indistinguishable and identical particles. While we have only paid lip service to the fact that each electron also possesses a spin angular momentum about its own axis, this became important at several points in the book, such as when we discuss superconductivity and Cooper pairs as well as at the end of the last chapter. When we deal with single isolated electrons, these approximations do not get us into very much trouble. However, most atoms and solids are densely populated with electrons, and the neglected properties can introduce new effects that need to be considered. Even though the effects may be quite small, an understanding of them is necessary, if for no other reason than to be able to ascertain when they may properly be ignored.
