Wave Functions for Quantum Harmonic Oscillators

Part of the Quantum Physics Workbook For Dummies Cheat Sheet

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:

image0.jpg

where

image1.jpg

And here’s the next-higher state:

image2.jpg

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

image3.jpg

where

image4.jpg
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