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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 field theory, the ground state is usually called the vacuum state or the vacuum. If more than one ground state exists, they are said to be degenerate. Many systems have degenerate ground states. Degeneracy occurs whenever there exists a unitary operator that acts non-trivially on a ground state and commutes with the Hamiltonian of ...
In other words, the degeneracy of every energy level is an even number if it has half-integer spin. The theorem is named after Dutch physicist H. A. Kramers . In theoretical physics, the time reversal symmetry is the symmetry of physical laws under a time reversal transformation:
In inorganic chemistry, crystal field theory (CFT) describes the breaking of degeneracies of electron orbital states, usually d or f orbitals, due to a static electric field produced by a surrounding charge distribution (anion neighbors).
Degeneracy See "degenerate energy level". Degenerate energy level If the energy of different state (wave functions which are not scalar multiple of each other) is the same, the energy level is called degenerate. There is no degeneracy in a 1D system. Energy spectrum The energy spectrum refers to the possible energy of a system.
Degeneracy (mathematics), a limiting case in which a class of object changes its nature so as to belong to another, usually simpler, class; 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
He derived equations for the line intensities which were a decided improvement over Kramers's results obtained by the old quantum theory. While the first-order-perturbation (linear) Stark effect in hydrogen is in agreement with both the old Bohr–Sommerfeld model and the quantum-mechanical theory of the atom, higher-order corrections are not. [9]