#PhysicsFactlet
A quantum simple pendulum.
The pendulum position is spread out, with opacity here being proportional to the probability that the pendulum is at that position at a given time. The average position of the quantum dynamics is the same as the classical pendulum dynamics (Ehrenfest theorem).
Technicalities: I used the Crank-Nicholson method to evolve the system in time. This is a 1D problem, and the only variable I considered was the angle, with the initial state being a Gaussian.
@j_bertolotti I'm confused because of the assumption that it's a 1D problem but it's shown in 2D. In 2D, I would expect the classical (average) position to not lie on the trajectory of the quantum positions. Essentially, I'm trying to figure out what's realistic about it and what isn't (like, is there any quantum mechanics in 1D anyway?)
@mjambon The (classical) simple pendulum itself is not realistic, but a simplified toy model used to make the math manageable.