# 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!

Related Quantum Physics News on Phys.org

#### tiny-tim

Homework Helper
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.

### Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving