Basic Physics Course with MATLAB's Symbolic Toolbox and Live Editor
Animation 6: Superposition of bound states
The Schrödinger equation with a Woods-Saxon potential is considered for negative energies. A base is constracted symbolically, the eigen value problem is solved numerically. We consider the superposition of the ground state ψ(1) and the first excited state ψ(2).
The time dependence of the probability density ρ is animated.
Only for mixed states (α≠0 and α≠π/2) ρ oscillates. For pure states (α=0 or α=π/2) ρ is stationary.