Degeneracy in the spectrum and features of the solution
PROFESSOR: If you tell someone solve this equation for l equals zero-- so you have this effective potential for the real equation-- solve it for l equals zero and you find some energies. You solve it for l equals 1, and you've found some energies. You solve it now for l equals two and you found some energies. Well, we found them all together, but something extraordinary happened there was no a priori reason the system should have been so simple. It might have happened that these states would have not been aligned with the previous states. Nothing we've explained in this course predicts that this would have happened, this perfect alignment with extreme amount of degeneracy. Because you have an l equals 2 multiplet here. That means five states. So there is degeneracy, but that's implicit in angular momentum. It has an explanation. But why would there be a degeneracy between l equals 1 solutions and l equals 2 solutions? Total mystery, actually. And this led to a...