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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. The number of different states corresponding to a particular energy level is known as the degree of degeneracy (or simply the degeneracy) of the level.
While degeneracy pressure usually dominates at extremely high densities, it is the ratio between degenerate pressure and thermal pressure which determines degeneracy. Given a sufficiently drastic increase in temperature (such as during a red giant star's helium flash ), matter can become non-degenerate without reducing its density.
In quantum mechanics terminology, the degeneracy is said to be "lifted" by the presence of the magnetic field. 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.
Degeneracy occurs whenever there exists a unitary operator which acts non-trivially on a ground state and commutes with the Hamiltonian of the system. According to the third law of thermodynamics , a system at absolute zero temperature exists in its ground state; thus, its entropy is determined by the degeneracy of the ground state.
is the degeneracy of energy level i, that is, the number of states with energy which may nevertheless be distinguished from each other by some other means, [nb 1] μ is the chemical potential, k is the Boltzmann constant, T is absolute temperature,
The degeneracy is preserved through first order by differential displacements that are perpendicular to the branching space. The space of non-degeneracy-lifting displacements, which is the orthogonal complement of the branching space, is termed the seam space. Movement within the seam space will take the molecule from one point of conical ...
Also acid ionization constant or acidity constant. A quantitative measure of the strength of an acid in solution expressed as an equilibrium constant for a chemical dissociation reaction in the context of acid-base reactions. It is often given as its base-10 cologarithm, p K a. acid–base extraction A chemical reaction in which chemical species are separated from other acids and bases. acid ...
In the case of degenerate energy levels, we can write the partition function in terms of the contribution from energy levels (indexed by j) as follows: =, where g j is the degeneracy factor, or number of quantum states s that have the same energy level defined by E j = E s.