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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.
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 ...
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 ...
t. e. A quantum mechanical system or particle that is bound —that is, confined spatially—can only take on certain discrete values of energy, called energy levels. This contrasts with classical particles, which can have any amount of energy. The term is commonly used for the energy levels of the electrons in atoms, ions, or molecules, which ...
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.
Energy levels can cross due to underlying symmetries of motion in the Coulomb potential. The Stark effect is the shifting and splitting of spectral lines of atoms and molecules due to the presence of an external electric field. It is the electric-field analogue of the Zeeman effect, where a spectral line is split into several components due to ...
Electron degeneracy pressure. In astrophysics and condensed matter physics, electron degeneracy pressure is a quantum mechanical effect critical to understanding the stability of white dwarf stars and metal solids. It is a manifestation of the more general phenomenon of quantum degeneracy pressure. In metals and white dwarf stars, electrons can ...
The free radical theory of aging states that organisms age because cells accumulate free radical damage over time. [1] A free radical is any atom or molecule that has a single unpaired electron in an outer shell. [2] While a few free radicals such as melanin are not chemically reactive, most biologically relevant free radicals are highly ...