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| pauli exclusion principle | |
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Because all observables are proportional to square of modulus of Wavefunction then in order to preserve the square the wave function of a system of Identical Particles must either remain the same, or must change sign to the opposite upon such exchange. Particles for which wave function does not change sign upon exchange are called Bosons , or particles with Symmetric wave function. The particles for which wave function of system changes sign to the opposite are called Fermion s, or particles with Antisymmetric wave function. Fermions therefore obey different statistics (called Fermi-Dirac statistics) than bosons (which obey Bose-Einstein statistics). One of consequences of Fermi-Dirac statistics is exclusion principle for fermions - no two fermions can share same quantum state (by other words, wave function of two fermions being at the same state is zero). This in turn results in Degeneracy Pressure for fermions - strong resistance of fermions to compression into smaller volume. This resistance gives rise to "stiffness" or "rigidity" of ordinary atomic matter (as atoms consists of electrons being fermions). Because the exchange of two identical particles is mathematically equivalent to the rotation of each particle by 360 degrees, the symmetricity of wave function depends on particle's Spin . Integer spin particles do not change the sign of their wave finction upon 360 degree rotation - therefore belong to bosonic family, while semi-integer spin particles change the sign of their wave function to the opposite upon 360 degree rotation thus belong to fermionic family. See more in Spin-statistics Theorem . |
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