Is There a Connection Between QHO and Angular Momentum?

[nateHI]

I watched a lecture that derived the properties of the angular momentum operators J and J3 using two QHOs and a bunch of algebra. The initial assumption was that two independent QHOs somehow correspond to angular momentum and everything was derived from there. I understand all the algebra (pretty basic stuff) but I don't understand the initial assumption.

Or, am I way off base and is the only relation between angular momentum and two independent QHOs that the two oscillators satisfy the J plus and J minus operator algebra?

You can see the lecture here if you want (AM stuff is 27 minutes in).
http://www.youtube.com/watch?v=dCua1R9VIiQ&feature=channel

 

[DrClaude]

Or, am I way off base and is the only relation between angular momentum and two independent QHOs that the two oscillators satisfy the J plus and J minus operator algebra?

That's the crux of it. You get the same algebra for angular momentum than for two harmonic oscillators (with a particular definition of $J_+$ and $J_-$ using the ladder operators of the QHOs), therefore studying the two QHOs will tell you about how angular momentum behaves.

The link between the two is derived in the sequence from 35 to 47 min. in the video.