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Degenerate energy levels. In quantum mechanics, an energy level is degenerate if it corresponds to two or more different measurable states of a quantum system. Conversely, two or more different states of a quantum mechanical system are said to be degenerate if they give the same value of energy upon measurement.
Degeneracy is the redundancy of the genetic code. This term was given by Bernfield and Nirenberg. The genetic code has redundancy but no ambiguity (see the codon tables below for the full correlation). For example, although codons GAA and GAG both specify glutamic acid (redundancy), neither specifies another amino acid (no ambiguity). The ...
Degenerate matter is usually modelled as an ideal Fermi gas, an ensemble of non-interacting fermions. In a quantum mechanical description, particles limited to a finite volume may take only a discrete set of energies, called quantum states. The Pauli exclusion principle prevents identical fermions from occupying the same quantum state.
Degeneracy (graph theory), a measure of the sparseness of a graph. Degeneration (algebraic geometry), the act of taking a limit of a family of varieties. Degenerate bilinear form, a bilinear form on a vector space V whose induced map from V to the dual space of V is not an isomorphism. Degenerate distribution, the probability distribution of a ...
Degeneracy (biology) Within biological systems, degeneracy occurs when structurally dissimilar components/pathways can perform similar functions (i.e. are effectively interchangeable) under certain conditions, but perform distinct functions in other conditions. [1] [2] Degeneracy is thus a relational property that requires comparing the ...
In the presence of more than one unpaired electron, the electrons mutually interact to give rise to two or more energy states. Zero field splitting refers to this lifting of degeneracy even in the absence of a magnetic field. ZFS is responsible for many effects related to the magnetic properties of materials, as manifested in their electron ...
Kramers' theorem. In quantum mechanics, the Kramers' degeneracy theorem states that for every energy eigenstate of a time-reversal symmetric system with half-integer total spin, there is another eigenstate with the same energy related by time-reversal. In other words, the degeneracy of every energy level is an even number if it has half-integer ...
In mathematics, a degenerate case is a limiting case of a class of objects which appears to be qualitatively different from (and usually simpler than) the rest of the class; [1] " degeneracy " is the condition of being a degenerate case. [2] The definitions of many classes of composite or structured objects often implicitly include inequalities.