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Could someone clear up the paper on casimir effect

  1. Nov 11, 2013 #1
    Hello,

    could someone please explain to me what happens between (3.6) and (3.7). In specific, I don't understand how substitution results in l^2/pie^2 and also what do they mean integrating over radial angle. And the x next to the dx at (3.7), where did it come from.

    http://aphyr.com/data/journals/113/comps.pdf

    Thank you!
     
  2. jcsd
  3. Nov 12, 2013 #2
    anyone?
     
  4. Nov 12, 2013 #3

    atyy

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    I didn't look that carefully but xdx is because x is a radial variable, so in the change of coordinates from Cartesian to polar, we usually get rdrdθ, where r is the Jacobian for the change of variables - they use x where I wrote r. The dθ doesn't appear becuase it has been integrated over already. Originally, they integrated over positive values of nx and ny, which are the original Cartesian coordinates. This is the first quadrant, ie. θ=0 to θ=∏/2.
     
    Last edited: Nov 12, 2013
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