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: $$\psi$$(r,t)= e^i(kr-$$\omega$$t), under the constraint that -k^2 + $$\omega$$^2/c^2 = m^2c^2/$$\hbar$$^2, forgive my lack of latex hah.

Through Euler's law this does give a solution tantamount to cos(kr-$$\omega$$t)+isin(kr-$$\omega$$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!

… 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.

no, the probability is ψ*ψ, not ψ²

 

[benk99nenm312]

hey benk99nenm312!


no, the probability is ψ*ψ, not ψ²

Omg wowww, lol. Thank you hah.