Hi,
i regard a single harmonic oszillator: $$H_{1}=\frac{p^{2}}{2m} + \frac{m \omega^{2}}{2} x^{2}$$
I know the partition function of the oszillator is: $$Z=\frac{kT}{\hbar \omega}$$
so the probability function is: $$F_{1}(x,p)=\frac{1}{Z}\exp{\frac{-H_{1}(x,p)}{kT}}$$
Now I want to callculate the average kinetic energy. So, can i do this? :$$
<\frac{p^2}{2m}>=\int\limits_{-\infty}^\infty dx \int \limits_{-\infty}^\infty dp~~~ F_{1}(x,p) \frac{p^2}{2m}
$$
i regard a single harmonic oszillator: $$H_{1}=\frac{p^{2}}{2m} + \frac{m \omega^{2}}{2} x^{2}$$
I know the partition function of the oszillator is: $$Z=\frac{kT}{\hbar \omega}$$
so the probability function is: $$F_{1}(x,p)=\frac{1}{Z}\exp{\frac{-H_{1}(x,p)}{kT}}$$
Now I want to callculate the average kinetic energy. So, can i do this? :$$
<\frac{p^2}{2m}>=\int\limits_{-\infty}^\infty dx \int \limits_{-\infty}^\infty dp~~~ F_{1}(x,p) \frac{p^2}{2m}
$$