Derive Equation of motion using Lagrangian density?

[safekhan]

Homework Statement [/b]

The attempt at a solution[/b]

I have done the first bit but don't know how to show that phi(r,t) is a solution to the equation of motion.

 

[George Jones]

Substitute the given $\phi$ into the left side of your equation; substitute the given $\phi$ into the right side of your equation. After doing this, show that left = right.

Equivalently, but perhaps a little cleaner: take all your terms to the left side; show that substituting $\phi$ into the left side gives zero.

 

[safekhan]

thanks, but how should I treat p.r term in the solution while differentiating with respect to (t,x,y,z)

 

[George Jones]

thanks, but how should I treat p.r term in the solution while differentiating with respect to (t,x,y,z)

What does

$$\mathbf{p} \cdot \mathbf{r}=?$$