In my freshman Chem 101 course, we are going over the development of the atomic model upto the basic modern quantum model. I learned that the azimuthal and magnetic quantum numbers were introduced to explain the fine spectrum of hydrogen and Zeeman/stark effects. Those numbers are still used today in modern quantum mechanics. But these numbers were derived using some classical mechanics and reasoning that ( as far as I know) don't fit in with modern quantum mechanics. So is it just that we have kept the numbers and their basic concept while disregarding the full original reasoning behind them?
And also, Bohr's model dealt with one electron systems. But the discussion in class moved from Bohr to these quantum numbers (to explain said effects) and then -out of nowhere- we applied these numbers to multi-electron systems. Were these numbers , back when they were invented, used for multi-electron systems?