Schrödinger equation eigenstates — shooting method on a finite square well
Using dimensionless units (ℏ=2m=1). The shooting method integrates ψ″ = (V(x)−E)ψ from the left boundary. An eigenstate exists when ψ→0 at the right boundary. The first 4 bound states ψₙ(x) are shown scaled by their energy level, plotted atop the potential V(x).