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Pendulum & Partition Function Problem

  1. Dec 4, 2011 #1
    1. A pendulum of mass m hangs from a weightless string of length l
    The string makes an angle θ with the vertical

    (i) <θ>
    (ii) <θ^2>
    (iii) <v>
    (iiii) <v^2>

    2. Relevant equations
    The Hamiltonian in terms of θ and the angular momentum L=

    H= L^2/2ml^2 + mgl(1-cosθ)

    3. The attempt at a solution
    I have the Hamiltonian derived for the pendulum
    I am unsure how to derive the partition function in terms of the angular momentum and θ from the equation
    Z=e^(-βH) where H is the Hamiltonian and β=1/T
  2. jcsd
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