We may therefore separate variables and look for solutions of the form . We will show that the are unique. To have a normalized wave function we need . It is convenient to normalize in the following way , . The normalized common eigenfunctions of L 2 and L z are called the spherical harmonics .
Separation of variables is possible.
We look for solutions of the form . Wave functions must be continuous at all points in space. We therefore need . In the case of orbital angular momentum the nature of the physical problem dictates that m must be an integer, and therefore l must be an integer. Y ll is uniquely defined up to the arbitrary constant c l .