The former quantum numbers can be related to the latter.
A number of modes are shown below together with their quantum numbers.
These are all the quantum numbers that the system can have.
Thus another set of quantum numbers should be used.
Every atomic species has associated with it a set of quantum numbers.
These are allowed to be indistinguishable, and they can all have the same quantum numbers including position.
The quantum numbers came first then from people looking at how light is absorbed by gases.
See for a group theoretical interpretation of these quantum numbers this article.
No two electrons can have the same set of quantum numbers.
The states are labeled by a set of quantum numbers.
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