Background: The problem develops further experience with the method of separation of variables, and will become useful when we treat the formal quantum mechanics of the Hydrogen atom.
The Time Independent Schrödinger Equation (TISE) for the Hydrogen atoms reads, in spherical coordinates,
Assignment:
Use the method of separation of variables to show that if we assume the form
, then the functions
, 
, and 
must obey the equations
where m and 
, for now, are the names given to arbitrary
constants produced by the separation procedure.