# A Time Independent form of Klein Gordon equation. How?

Tags:
1. Oct 4, 2016

### Mohanraj S

If equation of motion(K-G Eqn.,) follows,
μμΦ+m2Φ=ρ
where 'ρ' is point source at origin.

How time independent form of above will become,
(∇2-m2)Φ(x)=gδ3(x)
where g is the coupling constant,
δ3(x) is three dimensional dirac delta function.

Last edited: Oct 4, 2016
2. Oct 4, 2016

### DuckAmuck

Remember the Minkowski metric is involved here:

$$\partial_\mu \partial^\mu = \partial_t^2 - \partial_x^2 - \partial_y^2 - \partial_z^2$$

There's no time dependence so:
$$\partial_t \Phi = 0$$

Then to get the source term:
$$\rho = -g\delta(x)^3$$

3. Oct 4, 2016

4. Oct 5, 2016

### DuckAmuck

That's what rho needs to be to get the equation you have. To have a point source, you use a dirac delta with some kind of charge or coupling.