Two Wells System

Setting $\beta = -1$ dramatically changes the shape of the potential. It becomes a Two Wells Potential.

This potential harbors two minima at $x$ = +1 and -1 ( $\alpha = 1.0$ ) and a maximum at $x = 0$. The phase space portrait of the solution of this problem is very different than that of the single well problem.

Exercise #5:

Write a 2 wells setup code to generate initial conditions to launch trajectories that will illustrate the behavior of the solutions of the Two Wells Potential. These initial conditions will be fed into the ODE solving code. These initial conditions should be sprinkled along the $x$ axis between the wells and to the right of the wells.

Use $\alpha = 1.0$, $\beta = -1$, $\mu = 0.0$, $A = 0.0$ and $\omega = 1$ in the code implementing the RK4 solution of Duffing Oscillator.

Check that the energy is conserved, i.e., constant, for each trajectory.