Calculation of Wave Functions in a Symmetrical Crystalline Field

It is possible to calculate the splitting of the energy levels of an ion caused by a crystalline field of a certain symmetry in a more systematic way. Instead of solving the secular equation, certain algebraic quantities, i.e., the idempotent elements of the ring of the group, are introduced which contain all the information that can be obtained from the symmetry. This makes it possible to state, before other physical arguments are introduced, how many parameters enter a particular problem. In order to make the method easy to handle, some tables have been added, and a special case has been worked out.