QUANTUM HARMONIC OSCILLATOR

The real (cyan) and imaginary (magenta) parts of the wave function of a quantum harmonic oscillator. The time-independent Schrödinger equation is solved with a shooting method to obtain the first 16 eigenfunctions, by which an initial wave function is approximated, and time evolution is applied. The initial wave function here is exp(-x2), scaled horizontally, shifted to the right, and normalised.