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I am struggling with the process of deducing a phase portrait from pseudopotential vs $x$ plot. Is there a resource that would be helpful in understanding it better?

Given the pseudopotential(V) vs $x$ in the figure:

V vs x

For different energy levels E(y= -4) = E1; E(y=0) = E2; E(y=4) = E3

I there a way to plot the phase portrait $\dot{x}$ vs $x$?

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  • $\begingroup$ the kinetic energy goes as velocity squared, so think about drawing the lines of equipotential for a 3d graph which is something like z = y^2 + x^3 $\endgroup$ – user1379857 Dec 12 '20 at 4:37
  • $\begingroup$ More specifically, on a graph with axes $x$ and $\dot x$, graph $m \dot x^2 / 2 + k x^3 = const$ for different constants. $\endgroup$ – user1379857 Dec 12 '20 at 5:01
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Here's some python code for generating phase planes

enter image description here

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