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Degeneracy plays a fundamental role in quantum statistical mechanics. For an N -particle system in three dimensions, a single energy level may correspond to several different wave functions or energy states. These degenerate states at the same level all have an equal probability of being filled.
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.
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.
A neurodegenerative disease is caused by the progressive loss of neurons, in the process known as neurodegeneration. [2][3] Neuronal damage may also ultimately result in their death. Neurodegenerative diseases include amyotrophic lateral sclerosis, multiple sclerosis, Parkinson's disease, Alzheimer's disease, Huntington's disease, multiple ...
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.
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. The term "degenerate" here is not related to ...
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 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 ...