ABSTRACT
This chapter gives several examples of educational value. They both involve simple one-dimensional calculations which can be treated numerically, but they illustrate basic principles which are of value in quantum chemistry and in solid state physics. By using more flexible trial wavefunctions, of course, the variational approach can be made quite accurate; it will always give upper bounds to the eigenvalues, since two states being studied are ground states, one for even parity and other for odd parity. The theory sketched is usually called the nearly-free electron theory. Since it takes the lattice potential to be a weak perturbation, it was supposed for a long time that it would not be of much use for electrons in a real metal, where the periodic potential is estimated to be strong. However, modern work has shown that the approach can be used for the conduction electrons in many metals if a weak effective potential is used in the one-electron Schrödinger equation.
