Quantum VS Classical Pendulum

Quantum VS Classical Pendulum
In this simulation, the classical pendulum (CP) is represented by the blue line, and the quantum pendulum (QP) is depicted by its probability density |ψ(θ)|² in black. The grey dotted line indicates its origin (e.g., where ψ(θ)=0). The upper left graph shows the angle of the CP and the mean angle of the QP. The grey area represents the uncertainty in the QP's position. The bottom left graph shows the same information in momentum space.
The first part of the video features an initial angle of 3π/4 (using a Gaussian packet for the QP). The second part is for π/6 (harmonic oscillator regime).
The CP dynamics (with no friction) are solved using a 4th-order Runge-Kutta method. The QP dynamics are solved by computing the eigenvectors for the single-particle potential V(θ) = mgL(1 - cos(θ)), then using Schrödinger's equation.
Parameters :
m = 1
g = 9.81
L = 1
h = 2pi

[@jaydenchan3568]

What exactly does the black line represent if it's a probability distribution?

[@RealCrafter645]

take an integral over the probability (squared wavefunction) times the position and voila