Morse potential

  1. I have the equation for the Morse potential, U = E_0 (1-exp(-a(r-r_0))^2. I'm asked to show that near the minimum of the curve the potential energy is a parabolic function. I've tried to play around with the taylor series with no hope! :( :(

    Many thanks, James
  2. jcsd
  3. nrqed

    nrqed 3,107
    Science Advisor
    Homework Helper
    Gold Member

    It is indeed just a simple Taylor expansion! Can you show your work?
    The potential vanishes at r=r_0 and the derivative of the potential also vanishes at r=r_0. The second derivative does not vanish at that point so you get that U(r) is approximately U''(r=r_0)/2 r^2 so a parabolic function.

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