degeneracy (redirected from Degeneracy (disambiguation))

degeneracy [di′jen·ə·rə·sē]

(mathematics)

The condition in which two characteristic functions of an operator have the same characteristic value.

(physics)

The condition in which two or more modes of a vibrating system have the same frequency; a special case of the mathematics definition.

(quantum mechanics)

The condition in which two or more stationary states of the same system have the same energy even though their wave functions are not the same; a special case of the mathematics definition.

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Degeneracy (quantum mechanics)

A term referring to the fact that two or more stationary states of the same quantum-mechanical system may have the same energy even though their wave functions are not the same. In this case the common energy level of the stationary states is degenerate. The statistical weight of the level is proportional to the order of degeneracy, that is, to the number of states with the same energy; this number is predicted from Schrödinger's equation. In quantum mechanics and in other branches of mathematical physics, the term degeneracy is employed also to characterize the eigenvalues of operators other than the energy operator. See Eigenvalue (quantum mechanics)