The first chapter is a brief review of the fundamental definitions of group theory; the second treats in some detail the representations of finite groups; and in the third, we indicate the essential properties of space groups associated with crystals.
After having given briefly in Chap. 4 the principle of the Ritz variational method, we study in Chap. 5 the symmetry properties of the eigenfunctions of the Schroedinger equation applied to a system with which we associate a finite symmetry group. Then we show how to choose the trial functions involved in the Ritz method, thus finding the symmetric functions which enable us to factor the secular determinant and solve the problem.
The principle of the fertile method of plane waves is developed in Chap. 6. Finally, we apply these ideas to an example: the determination of energy levels in a diamond-type crystal.
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