Monte Carlo in the microcanonical ensemble

Integration of the kinetic degrees of freedom

Considering a system of $\left.N\right.$ identical particles, with total energy $\left.H\right.$ given by:

$H=\sum _{i=1}^{3N}{\frac {p_{i}^{2}}{2m}}+U\left(X^{3N}\right).$

where the first term on the right hand side is the kinetic energy, whereas the second one is the potential energy (function of the position coordinates)

From the partition function in the microcanonical ensemble we can integrate

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