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However, stability of large systems with many electrons and many nucleons is a different question, and requires the Pauli exclusion principle. [ 15 ] It has been shown that the Pauli exclusion principle is responsible for the fact that ordinary bulk matter is stable and occupies volume.
The first solution to this problem was provided by Freeman Dyson and Andrew Lenard in 1967–1968, [1] [2] but a shorter and more conceptual proof was found later by Elliott Lieb and Walter Thirring in 1975 using the Lieb–Thirring inequality. [3] The stability of matter is partly due to the uncertainty principle and the Pauli exclusion ...
Fermi–Dirac statistics applies to fermions (particles that obey the Pauli exclusion principle), and Bose–Einstein statistics applies to bosons. As the quantum concentration depends on temperature, most systems at high temperatures obey the classical (Maxwell–Boltzmann) limit, unless they also have a very high density, as for a white dwarf.
The spin–statistics theorem of quantum field theory demands that all particles with half-integer spin behave as fermions and all particles with integer spin behave as bosons. Multiple bosons may occupy the same quantum state; however, by the Pauli exclusion principle, no two fermions can occupy the same state
While the Pauli principle and Fermi-Dirac distribution applies to all matter, the interesting cases for degenerate matter involve systems of many fermions. These cases can be understood with the help of the Fermi gas model. Examples include electrons in metals and in white dwarf stars and neutrons in neutron stars.
The Fermi–Dirac distribution is only valid if the number of fermions in the system is large enough so that adding one more fermion to the system has negligible effect on μ. [15] Since the Fermi–Dirac distribution was derived using the Pauli exclusion principle , which allows at most one fermion to occupy each possible state, a result is ...
The Pauli exclusion principle is the quantum mechanical principle that states that two identical fermions (particles with half-integer spin) cannot occupy the same quantum state simultaneously. Subcategories
Pauli introduced the 2×2 Pauli matrices as a basis of spin operators, thus solving the nonrelativistic theory of spin. This work, including the Pauli equation , is sometimes said to have influenced Paul Dirac in his creation of the Dirac equation for the relativistic electron, though Dirac said that he invented these same matrices himself ...