Submicroscopic harmonic oscillators are popular quantum physics problems because harmonic oscillators are relatively simple systems — the force that keeps a particle bound here is proportional to the distance that the particle is from the equilibrium point.

Here’s the harmonic oscillator at its simplest:

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where

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And here’s the next-higher state:

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In general, you can use the following equation for the wave functions, where Hn is a hermite polynomial:

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where

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