- #1

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I don't understand why we need to imagine this varied path, why not differentiate the original path?

- Thread starter NihalRi
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- #1

- 134

- 12

I don't understand why we need to imagine this varied path, why not differentiate the original path?

- #2

ShayanJ

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The answer in both cases is that we need to find out in what point the derivative is equal to zero to lowest order, which means the function doesn't change when we move only a little bit. You just need to recognize that an action integral is a function of paths between two given endpoints so when we want to calculate its derivative, we have to consider two nearby paths between those two endpoints(like ##x+\delta## and ##x## above) and calculate the output of the action integral for both and demand that the difference vanishes to lowest order. This way we find out at what path this happens and that'll be the correct path. This is pretty much like setting the first derivative of a function of one variable to zero to find in what ##x##s the function has extrema.

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Ssnow

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