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## Main Question or Discussion Point

Hi everyone,

I've been reading about the Klein Gordon equation with the Coulomb Potential. The full solution can be found here:

http://wiki.physics.fsu.edu/wiki/index.php/Klein-Gordon_equation#Klein-Gordon_equation_with_Coulomb_potential

I'm confused near the beginning of this. I understand that the solution is going to look like

$$\Phi(r,t) = R(r)Y(\theta,\phi)T(t)$$

since this is radially symmetric and a second order linear homogeneous partial differential equation, so it is separable. What I don't understand is why all the solutions I look at assume

$$T(t)=e^{-iEt/\hbar}.$$

I've looked up a number of solutions and they all make this assumption without explanation, so I'm assuming I'm missing something obvious. Can anyone explain it to me?

Thanks!

I've been reading about the Klein Gordon equation with the Coulomb Potential. The full solution can be found here:

http://wiki.physics.fsu.edu/wiki/index.php/Klein-Gordon_equation#Klein-Gordon_equation_with_Coulomb_potential

I'm confused near the beginning of this. I understand that the solution is going to look like

$$\Phi(r,t) = R(r)Y(\theta,\phi)T(t)$$

since this is radially symmetric and a second order linear homogeneous partial differential equation, so it is separable. What I don't understand is why all the solutions I look at assume

$$T(t)=e^{-iEt/\hbar}.$$

I've looked up a number of solutions and they all make this assumption without explanation, so I'm assuming I'm missing something obvious. Can anyone explain it to me?

Thanks!