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Derive Equation of motion using Lagrangian density?

  1. Nov 10, 2013 #1
    The problem statement, all variables and given/known data[/b]

    q1.png



    The attempt at a solution[/b]
    ans.jpg

    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.
     
  2. jcsd
  3. Nov 10, 2013 #2

    George Jones

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    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.
     
  4. Nov 11, 2013 #3
    thanks, but how should I treat p.r term in the solution while differentiating with respect to (t,x,y,z)
     
  5. Nov 11, 2013 #4

    George Jones

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    What does

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