1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Comparing differentials

  1. Feb 19, 2013 #1
    I recently did a problem with some electron constraint to move on a hoop. It kind of surprised me that you just could take the old Schrödinger-equation with and let your
    dx ->dβ, where β is the distance along the hoop.
    Saying it in a less mathematical way, isn't a differential distance along something curved larger than a differential distance in a fixed direction? I do realize that a rigorous mathematician would shoot me for saying something like this, so how would he say it?
  2. jcsd
  3. Feb 19, 2013 #2
    In a problem like this the best suited thing to do is to pass to polar coordinates, so you can describe a loop more simply. Then in these coordinates with origin at the center of the loop which is at a fixed radius r, you have [itex]dx^2+dy^2=r^2d\theta^2=d\beta^2[/itex]. So it's simply the old good polar coordinates.
  4. Feb 19, 2013 #3
    Remember this? ## \displaystyle \lim_{x \rightarrow 0 } \frac {\sin x} {x} = 1 ##.

    It ensures that the length of a chord and the corresponding arc are about the same when they are small, let alone differential. It might be useful for you to follow the proof of the statement.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook