Wow! Here's the short version of what's going on. My quantum II final was a bit rough because I didn't know how to decouple a pair of coupled harmonic oscillators. However, I found an excellent article on decoupling in my second favorite journal the American Journal of Physics. I wanted to capture a few notes here on the process and on one of the math operations left out of the original article, but hashing out the level of background to provide has taken awhile. I decided to go with the terser representation of the subject. It may be extremely sketchy since I'm more than a bit scattered studying for finals. Basically, these are my notes, and I hope they're helpful :) Any ideas, comments, corrections, or suggestions, as always, are more than welcome! For more detail and an excellent article on how to decouple coupled oscillators see [1]. OK, here goes. What does 'decoupling harmonic oscillators' mean and what is it ...