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Jay Wang
Nov 6, 2017, 2:22:33 PM11/6/17
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The central field approximated potential, Eq. (4.30), is related to the elliptic integral (EI), which is usually expressed in terms of sin(theta) [See Appendix 11.B for EI]. To make the connection, realize that the integral in Eq. (4.30) is equal to 2 int_0^pi dx /sqrt(1+r^2+2 r cos(x); note the change in sign in front of cos(x). Now use the trig identity
cos(2t) = 1 - 2 sin^2(t), where t=x/2, the integral can be brought to the form of EI, Eqs. (11.61) and (11.62).
cos(2t) = 1 - 2 sin^2(t), where t=x/2, the integral can be brought to the form of EI, Eqs. (11.61) and (11.62).
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