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Homework Statement
I have to sketch a phase portrait (in phase space) for a system which is a diatomic molecule. The effective potential is equal to a potential that is attractive at long range and repulsive at short range plus the centrifugal barrier. It basically looks like a Morse potential with a little "bump" right outside the potential well (due to centrifugal barrier).
Homework Equations
[tex] V_{eff}(r)=V(r)+ \frac{L^2}{2 \mu r^2}[/tex]
mu is the reduced mass, r is the distance between atoms and L is angular momentum (a constant)
The Attempt at a Solution
I wrote down Hamilton's equations (assuming a Morse or Lennard-Jones potential) and tried to put them on an applet for this kind of stuff but the results seem weird. For low energies I think the system will have an oscillatory motion (so ellipses will appear in phase space), but I'm kinda clueless about higher energies. I guess that given enough initial potential energy r will simply increase constantly and p will go through one maximum and one minimum. The equilibrium point will be the distance corresponding to the bottom of the well and the top of the bump. Can I get some help?