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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).

Gauss interference

Bound state

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 .