What is "quantum number"

n. (context quantum mechanics English) One of certain integers or half-integers that specify the state of a quantum mechanical system (such as an electron in an atom).

Quantum numbers describe values of conserved quantities in the dynamics of a quantum system. In the case of electrons, the quantum numbers can be defined as "the sets of numerical values which give acceptable solutions to the Schrödinger wave equation for the hydrogen atom". An important aspect of quantum mechanics is the quantization of observable quantities, since quantum numbers are discrete sets of integers or half-integers, although they could approach infinity in some cases. This distinguishes quantum mechanics from classical mechanics where the values that characterize the system such as mass, charge, or momentum, range continuously. Quantum numbers often describe specifically the energy levels of electrons in atoms, but other possibilities include angular momentum, spin, etc. Any quantum system can have one or more quantum numbers; it is thus difficult to list all possible quantum numbers.