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In 1940, Pauli proved the spin–statistics theorem, which states that fermions have half-integer spin, and bosons have integer spin. [7] In retrospect, the first direct experimental evidence of the electron spin was the Stern–Gerlach experiment of 1922. However, the correct explanation of this experiment was only given in 1927. [38]
t. e. In quantum mechanics, spin is an intrinsic property of all elementary particles. All known fermions, the particles that constitute ordinary matter, have a spin of 1 2 . [1][2][3] The spin number describes how many symmetrical facets a particle has in one full rotation; a spin of 1 2 means that the particle must be rotated ...
Fermi–Dirac statistics applies to identical and indistinguishable particles with half-integer spin (1/2, 3/2, etc.), called fermions, in thermodynamic equilibrium. For the case of negligible interaction between particles, the system can be described in terms of single-particle energy states. A result is the Fermi–Dirac distribution of ...
A composite particle (hadron) may fall into either class depending on its composition. In particle physics, a fermion is a particle that follows Fermi–Dirac statistics. Fermions have a half-odd-integer spin (spin 1/2, spin 3/2, etc.) and obey the Pauli exclusion principle. These particles include all quarks and leptons and all ...
The spin–statistics theorem proves that the observed relationship between the intrinsic spin of a particle (angular momentum not due to the orbital motion) and the quantum particle statistics of collections of such particles is a consequence of the mathematics of quantum mechanics. In units of the reduced Planck constant ħ, all particles ...
Equilibrium thermal distributions for particles with integer spin (bosons), half integer spin (fermions), and classical (spinless) particles. Average occupancy is shown versus energy relative to the system chemical potential , where is the system temperature, and is the Boltzmann constant.
Half-integer spin means that the intrinsic angular momentum value of fermions is = / (reduced Planck constant) times a half-integer (1/2, 3/2, 5/2, etc.). In the theory of quantum mechanics, fermions are described by antisymmetric states. In contrast, particles with integer spin (bosons) have symmetric wave functions and may share the same ...
The quantum Heisenberg model, developed by Werner Heisenberg, is a statistical mechanical model used in the study of critical points and phase transitions of magnetic systems, in which the spins of the magnetic systems are treated quantum mechanically. It is related to the prototypical Ising model, where at each site of a lattice, a spin ...
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