(adsbygoogle = window.adsbygoogle || []).push({}); 1. A pendulum of mass m hangs from a weightless string of length l

The string makes an angle θ with the vertical

Find

(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

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# Homework Help: Pendulum & Partition Function Problem

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