# Density distribution

1. Nov 23, 2004

Consider a system with one degree of freedom whose density distribution at time t=0 is given by:

$$D(x,p,t=0)=\frac{1}{\pi\sigma^2}exp[-\frac{m\omega^2}{2}x^2-\frac{1}{2m}p^2]$$

where $$x$$ is the generalized coordinate and $$p$$ the conjugate momentum. The Hamiltonian of the system is given by:

$$H=\frac{p^2}{2m}+V(x)$$

a) For $$V=\frac{1}{2}m\omega^2x^2$$ find the density distribution at time t. Choose a convenient area R in phase space and study the way it moves as a function of time.

b) Same question for $$V=0$$.

I don't even know how to start this problem. Any hints on where I can begin?