Quantum number is generally used in classical physics/ chemistry for showing momentum ,spin etc in atomic particles .
Further more I read it viz a refrence but again in terms of classical era .
A quantum number describes the energies of electrons in atoms.Each quantum number specifies the value of a conserved quantity in the dynamics of the quantum system.The most widely studied set of quantum numbers is that for a single electron in an atom: not only because it is useful in chemistry, being the basic notion behind the periodic table, valence (chemistry) and a host of other properties, but also because it is a solvable and realistic problem, and, as such, finds widespread use in textbooks.
As far as I have gone through the quantum physics the contemporary one I dont find something like Quantum Numbers , We av instead Qubits that you are well acquinted with .
Still if you get any more info regarding this please i would love to know and learn from you .
as far as I can find Information about Quantum Number it's a numerical classification of the Quantum State of quants. It consists of 4 numbers each of them representing a special Quantum Theory since BOHR.
It's interesting for Physicians who are working with many atoms and molecules and as you say in chemistry too.