Wave Functions for Quantum Harmonic Oscillators
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:
And here’s the next-higher state:
In general, you can use the following equation for the wave functions, where Hn is a hermite polynomial: