Quantum numbers

Article By:

Lassila, Kenneth E. Department of Physics, Iowa State University, Ames, Iowa.

Last reviewed:August 2020

DOI:https://doi.org/10.1036/1097-8542.563000

The quantities, usually discrete with integer or half-integer values, which are needed to characterize a physical system of one or more atomic or subatomic particles. Specification of the set of quantum numbers serves to define such a system or, in other words, to label the possible states the system may have. In general, quantum numbers are obtained from conserved quantities determinable by performing symmetry transformations consisting of arbitrary variations of the system which leave the system unchanged. For example, since the behavior of a set of particles should be independent of the location of the origin in space and time (that is, the symmetry operation is translation in spacetime), it follows that momentum and energy are rigorously conserved. In similar fashion, the invariance of the system to arbitrary rotations of the three axes defining three-dimensional space leads to conservation of total angular momentum. Inversion of these three axes through their origin is likewise a symmetry operation and leads to conservation of parity. (Parity is not conserved in weak interactions and cannot be used as a quantum number to specify the state of a set of particles undergoing such interactions. For such a case, parity is not a “good” quantum number.) For a list of invariance or symmetry operations and the corresponding conserved quantities See also: Symmetry laws (physics)

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