Your quantum physics instructor may ask you to find the energy level of a harmonic oscillator. The best way to learn how is through an example. Say that you have a proton undergoing harmonic oscillation with
![image0.png](https://www.dummies.com/wp-content/uploads/396258.image0.png)
as shown in the figure.
![A proton undergoing harmonic oscillation.](https://www.dummies.com/wp-content/uploads/396259.image1.jpg)
A proton undergoing harmonic oscillation.
What are the energies of the various energy levels of the proton? You know that in general,
![image2.png](https://www.dummies.com/wp-content/uploads/396260.image2.png)
So here are the energies of the proton, in megaelectron volts (MeV):
![image3.png](https://www.dummies.com/wp-content/uploads/396261.image3.png)
And so on.
Now what about the wave functions? The general form of
![image4.png](https://www.dummies.com/wp-content/uploads/396262.image4.png)
Convert all length measurements into femtometers
![image5.png](https://www.dummies.com/wp-content/uploads/396263.image5.png)
where x is measured in femtometers:
![image6.png](https://www.dummies.com/wp-content/uploads/396264.image6.png)
Here are a couple more wave functions:
![image7.png](https://www.dummies.com/wp-content/uploads/396265.image7.png)