Homework 1
1.) Mawell Boltzmann
Given the Maxwell -Boltzmann Distribution
- [math]N(v) = 4 \pi \left ( \frac{m}{2\pi kT}\right)^{3/2} v^2 e^{-\frac{mv^2}{2kT}}[/math]
a.) Show <v>
Show that
- [math]\lt v\gt = 4\pi \left ( \frac{m}{2 \pi kT}\right )^{3/2} \left( \frac{2kT}{m}\right)^2 \frac{\Gamma(2)}{2}[/math]
b.) Energy Fluctuation
Show that the energy fluctuation is
- [math]\frac{1}{4} m \lt \left ( v - \lt v\gt \right)^2\gt = \frac{3}{2} (kT)^2[/math]
2.) MC calculation of Pi
Calculate \pi using the Monte Carlo method described in the Notes
3.) Histograms using ROOT
Homework 2
Homework 3
Homework 4
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