I have asked many people and searched many sources for the answer to the following question but have yet to reach a satisfactory conclusion. When solving the hydrogen atom by separation of variables, for the angular equation, you come across the O.D.E. d^2/(do)^2 (F) = -m^2 * F where o is the polar angle. This is an easily solvable second order differential equation. The general solution is F(o) =A*e^imo + B*e^-imo where A and B are constants. The problem is all the textbooks I've looked at only have the first term and just say m can positive or negative. This is fine, but why can't it be a linear combination of the two? Why must it only be one term? I've looked at the boundary conditions and have found no reason. If we allow for a combination of terms, it changes the wavefunction so that must be wrong. But where's the problem? Thanks.