Oops sorry I miss wrote the integral in one of the lines above. It should read
\
Z=\int exp[ax^2+bxy+cy^2] d^{3n}x d^{3n}y
my problem happens to be specified that the exponential is of the form
\\x^2+(m w y)^2 + 2mwxyThis makes the matrix in the above solution singular and the integral...
I need to find the integral as follows:
I am given a Hamiltonian of the form:
\
H=\Sigma {(x_n+d y_n)^2}< 2 m E
(This should be a sum over n, but its not showing in the preview)
we integrate the exponential in n-space as
\
\begin{equation}
\int \exp{H} d^{3n}x d^{3n}y...