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The term "harmonic oscillator" is used to describe any system with a "linear" restoring force that tends to return the system to an equilibrium state. There is both a classical harmonic oscillator and a quantum harmonic oscillator. Both are used as toy problems that describe many physical systems.

14 votes

Eigenfunctions and energies of a quadratic-bottom finite square well

I see the fatal flaw here. Inside the well, your solution must be a solution to the HO, BUT there are two solutions to the HO. There is the one we're all familiar with, a hermite polynomial times a g …
James Johns's user avatar