any of several quantities of integral or half-integral value that identify the state of a physical system such as an atom, a nucleus, or a subatomic particle. Quantum numbers refer generally to properties that are discrete (quantized) and conserved, such as energy, momentum, charge, baryon number, and lepton number.

The principal quantum number for electrons confined in atoms, for example, indicates the energy state and the probability of finding the electrons at various distances from the nucleus. The larger the principal quantum number, which has integral values beginning with one, the greater the energy is and the farther the electron is likely to be from the nucleus. The principal quantum number and three others are sufficient to characterize uniquely each electron in an atom. Another set of quantum numbers characterizes the atomic nucleus.