Consider a system with one degree of freedom whose density distribution at time t=0 is given by:(adsbygoogle = window.adsbygoogle || []).push({});

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

where [tex]x[/tex] is the generalized coordinate and [tex]p[/tex] the conjugate momentum. The Hamiltonian of the system is given by:

[tex]H=\frac{p^2}{2m}+V(x)[/tex]

a) For [tex]V=\frac{1}{2}m\omega^2x^2[/tex] 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 [tex]V=0[/tex].

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

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# Homework Help: Density distribution

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