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.
Since any quantum system can have one or more quantum numbers, it is a futile job to list all possible quantum numbers.
The question of how many quantum numbers are needed to describe any given system has no universal answer, although for each system one must find the answer for a full analysis of the 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.
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