Derive Equation of motion using Lagrangian density?

  • Thread starter safekhan
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  • #1
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Homework Statement [/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.
 

Answers and Replies

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

What does

$$\mathbf{p} \cdot \mathbf{r}=?$$
 

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