Solution to the Klein Gordon Equation

benk99nenm312

Hey guys, I was reading up on the Klein Gordon equation and I came across an article that gave a general solution as: [tex]\psi[/tex](r,t)= e^i(kr-[tex]\omega[/tex]t), under the constraint that -k^2 + [tex]\omega[/tex]^2/c^2 = m^2c^2/[tex]\hbar[/tex]^2, forgive my lack of latex hah.

Through Euler's law this does give a solution tantamount to cos(kr-[tex]\omega[/tex]t)+isin(kr-[tex]\omega[/tex]t).

My question is simply.. is this valid? I ask because if you were to integrate the square over an interval you should get a probability, however the imaginary term will carry through from the de Moivre formula. I'm terribly confused.

Thanks guys!

tiny-tim

hey benk99nenm312!
no, the probability is ψ*ψ, not ψ²

benk99nenm312

Omg wowww, lol. Thank you hah.