# Mircocanonical Damped Harmonic Oscillator

1. Oct 18, 2010

I am supposed to find the number of mircostates for the following Hamiltonian

$$\ \Sigma {(q_n+mwp_n)^2}<2mE$$

So I am attempting to take the integral as follows

$$\ \int e^{(q_n+mwp_n)^2} d^{3n}q d^{3n} p [tex\] I found a solution that tells me [tex]\ \int \exp{(ax^2+bxy+cx^2)^2} d^{3n}x d^{3n}y$$

which equals

$$\ \pi^{m/2}/{det[A]}$$

where A is the 2-D matrix
A=[a b
b c]

However, the determinant is zero so this doesn't work. I found this solution at http://srikant.org/thesis/node13.html .
There is a bit more work shown on the website. My professor assured me that the solution is closed form.
PS.