Supermultiplet

Article By:

Iachello, Francesco Department of Physics, Yale University, New Haven, Connecticut.

Last reviewed:January 2021

DOI:https://doi.org/10.1036/1097-8542.669500

A generalization of the concept of a multiplet. A multiplet is a set of quantum-mechanical states, each of which has the same value of some fundamental quantum number and differs from the other members of the set by another quantum number which takes values from a range of numbers dictated by the fundamental quantum number. The number of states in the set is called the multiplicity or dimension of the multiplet. The concept was originally introduced to describe the set of states in a nonrelativistic quantum-mechanical system with the same value of the orbital angular momentum, L, and different values of the projection of the angular momentum on an axis, M. The values that M can take are the integers between −L and L, 2L + 1 in all. This is the dimension of the multiplet. If the hamiltonian operator describing the system is rotationally invariant, all states of the multiplet have the same energy. A supermultiplet is a generalization of the concept of multiplet to the case when there are several quantum numbers that describe the quantum-mechanical states. See also: Angular momentum; Symmetry laws (physics)

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