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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.
Degenerative disease is the result of a continuous process based on degenerative cell changes, affecting tissues or organs, which will increasingly deteriorate over time. [ 1 ] In neurodegenerative diseases, cells of the central nervous system stop working or die via neurodegeneration. An example of this is Alzheimer's disease. [ 2 ]
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.
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.
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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 ...
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