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Probability Density Function for a Pendulum?

  1. Oct 2, 2012 #1
    What is the probability density equation as a function of angle for a simple pendulum using the small angle approximation?
     
  2. jcsd
  3. Oct 2, 2012 #2
    Do you mean to treat the situation quantum mechanically? If so, then assume a potential:

    [tex] U(\phi) = mglsin(\phi) ≈ mgl\phi [/tex]

    Where l is the fixed distance from the origin this thing oscillates at. Then your Hamiltonian is given by:

    [tex] H = -\frac{\hbar^2}{2ml^2}\frac{d^2}{d\phi^2} + mgl\phi [/tex]

    Solve this with some boundary condition and you'll know.
     
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