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Potential energy approximation

  1. Feb 3, 2008 #1
    1. The problem statement, all variables and given/known data

    Find the linear harmonic oscillator approximation for potential energy function:

    [tex]\ V=[/tex][tex]\frac{a}{x^2}+[/tex][tex]\ b [/tex][tex]\ x^2 [/tex]

    2. Relevant equations

    3. The attempt at a solution

    The 2nd term will be present in the expression of V(approx).But what about the first term. Should we make it {1+(x-1)} and expand binomially?But that would involve two points of eqlbm---one is 0 and the other is 1...

    Can anyone please help?
    Last edited: Feb 3, 2008
  2. jcsd
  3. Feb 3, 2008 #2

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    Homework Helper

    You have to find the minimum first. If both a,b>0, then the minima occur at x= +-(a/b)^1/4. Take the +ve value, say. Expand the function as a Taylor series around that point and retain up to the x^2 term.

    Note that the function is not defined at x=0, and approaches infinity as x tends to zero. Why were you thinking of x=0 as an equilibrium point?
  4. Feb 3, 2008 #3
    Yes,I really made a mistake in undestanding the problem.Now, I can do it.Thank you very much.
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