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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.
Therefore, an electron in an atom emits light only when it is in a superposition of states.
The conventional image of an electron jumping from an excited state to a lower state to emit light is a great simplification, it is very much adapted to our idea of an objective world.
Further details can be found in Chap05_4 .