- Degenerate energy level
In physics, two or more different quantum states are said to be degenerate if they are all at the same energy level. Statistically this means that they are all equally probable of being filled, and in Quantum Mechanics it is represented mathematically by the Hamiltonian for the system having more than one linearly independent eigenstate with the same eigenvalue. Conversely, an energy level is said to be degenerate if it contains two or more different states. The number of different states at a particular energy level is called the level's degeneracy, and this phenomenon is generally known as a quantum degeneracy.
In quantum theory this usually pertains to electronic configurations and the electron's energy levels, where different possible occupation states for particles may be related by symmetry. For example, in the hydrogen atom, for a fixed energy eigenvalue, there exist several states which have that energy, but differ in the eigenvalues of angular momentum L2, spin component Sz and so on. The usage comes from the fact that degenerate eigenstates correspond to identical eigenvalues of the Hamiltonian. Since eigenvalues correspond to roots of the characteristic equation, degeneracy here has the same meaning as the common mathematical usage of the word.
In electromagnetics, degeneracy refers to modes of propagation which exist at the same frequency and longitudinal propagation constant. As an example, for a rectangular waveguide, the TEmn mode is degenerate to the TMmn mode if m and n are the same for both of them.
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non-degenerate energy level — neišsigimęs energijos lygmuo statusas T sritis fizika atitikmenys: angl. non degenerate energy level vok. unentartetes Energieniveau, n rus. невырожденный уровень энергии, m pranc. niveau d’énergie non dégénéré, m … Fizikos terminų žodynas
Energy level splitting — occurs in physics when the degenerate energy levels of two or more states are split because of external fields or other effects. The term is most commonly used in quantum theory in reference to the electron configuration in atoms or molecules.… … Wikipedia
Energy level — A quantum mechanical system or particle that is bound that is, confined spatially can only take on certain discrete values of energy. This contrasts with classical particles, which can have any energy. These discrete values are called energy… … Wikipedia
Degenerate orbital — See also: Degenerate energy level Degenerate orbitals for electrons in an atomic subshell are orbitals at identical energy levels. These are important in physical chemistry because they affect the ways electrons fill atoms (see Hund s rule). For… … Wikipedia
degenerate — I. adjective Etymology: Middle English degenerat, from Latin degeneratus, past participle of degenerare to degenerate, from de + gener , genus race, kind more at kin Date: 15th century 1. a. having declined or become less specialized (as in… … New Collegiate Dictionary
Degenerate orbitals — for electrons in an atomic subshell are orbitals at identical energy levels. These are important in physical chemistry because they affect the ways electrons fill atoms (see Hund s rule). For example, all the 3p orbitals have same energy level,… … Wikipedia
degenerate state — Usually, degenerate states. Physics. a quantum state of a system, having the same energy level as, but a different wave function from, another state of the system. [1925 30] * * * … Universalium
degenerate — adjective dɪ dʒɛn(ə)rət 1》 having lost the physical or moral qualities considered normal and desirable; showing evidence of decline. ↘Biology having reverted to a simpler form as a result of losing a structure present in the ancestral form.… … English new terms dictionary
degenerate state — Usually, degenerate states. Physics. a quantum state of a system, having the same energy level as, but a different wave function from, another state of the system. [1925 30] … Useful english dictionary
degenerate — degenerately, adv. degenerateness, n. v. /di jen euh rayt /; adj., n. /di jen euhr it/, v., degenerated, degenerating, adj., n. v.i. 1. to fall below a normal or desirable level in physical, mental, or moral qualities; deteriorate: The morale of… … Universalium