Of course, I understand, I mean I am currently doing field theory in particle physics and some arguments for plane wave solutions, for me, lack some structure, therefore I asked...I just wanted to get some more insight into some basics...
Yes, I understand that but aren't the things you said just consequences? It is like it bothers me in some fundamental QM way. I mean I can't be satisfied with the argument that it gives nice solutions. I mean, it is obviously correct considering the experiments in QM.
Why in order to derive the QM momentum operator we use the plane wave solution. Why later on in field theory and particle physics, the plane wave ansatz is so physically important?
Griffits and Jackson, that is standard literature for classical electrodynamics, write general solution for wave equation for monochromatic wave in complex notation. Sorry if I am a little bit confusing. I hope I explained my troubles better this time.