Ian Jauslin

$$U(x)=x^4-2a^2x^2,\qquad a=\frac12$$ The graphs below show the potential, and the phase space of a particle submitted to the double well potential. The energy can be adjusted with the slider below and exhibit the different types of motion:

- for $E\in(-a^2,0)$: oscillations around one well
- for $E\in(0,\infty)$: oscillations around both wells
- for $E=0$: separatrix: the system requires an infinite amount of time to reach 0. Because of numerical errors in the simulation the time is not infinite, but large.

Energy: E=-0.5