Hypnotoad
Nov23-04, 12:42 PM
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?
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?