Simulation of the time-dependent Schrödinger equation in one dimension illustrating the wave function behavior of stationary states and gaussian wave packets in a custom spline-like potential using periodic boundary conditions.

The system was expressed as a grid-based Hamiltonian system without complex numbers. The imaginary part was reformulated in the quadratic form Hamiltonian as real value conjugate momenta.

The 3D segments display the spatial coordinate along the first axis (x), and the canonical coordinates (q,p) associated with the wave function's real and imaginary part along the two other axes.

The system was simulated using high order explicit symplectic integrators and was simulated and rendered in real time.

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