Well, I'm off to take a course in quantum mechanics. I'll see everyone in 4.5 months... 
[spoiler]You won't need to know quantum mechanics, but it might help. You just need to know the rules. Have you used ALL of the clues?[/spoiler]
[spoiler]I've tried to obtain the inner product by multiplying each set of numbers. Not sure what to do with 231, 100, 600, 441, etc., though. Then I tried to take the average (mean) of each set of numbers. Again, no clue what to due with a number like 15.5. Wikipedia has not been tremendously helpful as a crash course in braketology. Tried to generalize things and find stuff related to Dirac and the harmony of the spheres, but nothing specific enough as an answer presents itself.[/spoiler]