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AI for Particle Physics
Published in Volker Knecht, AI for Physics, 2023
Mario Campanelli, Volker Knecht
Bosons behave according to Bose–Einstein statistics, in which several indistinguishable particles can assume the same state. In contrast, fermions obey the Pauli exclusion principle forbidding identical fermions from occupying the same quantum state simultaneously. This rule is the ultimate reason why ordinary matter occupies volume.
Linear Algebra for Quantum Mechanics
Published in Caio Lima Firme, Quantum Mechanics, 2022
If two rows or two columns of a determinant, D, are equal, then D = 0. Pauli exclusion principle states where two electrons are in the same orbital, then they cannot have the same spin-orbital. Then, in the Slater determinant, two rows or two spin-orbitals cannot be the same, i.e., f1 ≠ f2, otherwise, the Slater determinant (which represents the set of molecular orbital, MO, wave functions) is zero.
The Schrödinger Wave Equation
Published in Daniel D. Pollock, PHYSICAL PROPERTIES of MATERIALS for ENGINEERS 2ND EDITION, 2020
exists, the wavefunctions are termed antisymmetric. This change in sign comes about when the two electrons are interchanged. The interchange changes the state-space coordinates of the electrons and results in antisymmetric wave functions as shown below. This concept is an important factor that arises from the Pauli exclusion principle because electrons are prevented from having the same quantum numbers. Both symmetric and antisymmetric wave functions are employed in the derivation of band theory (Section 5.8).
Effects of quantum mechanical identity in particle scattering: experimental observations (and lack thereof)
Published in Journal of the Royal Society of New Zealand, 2021
In the quantum description of systems of particles two categories are encountered: particles with half-integer spin, called fermions, and particles with integer spin, called bosons. The quantum mechanical wave function for a system of identical bosons is required to be symmetric under the permutations of two particles. In contrast, the quantum mechanical wave function for a system of identical fermions is required to be antisymmetric under the permutations of two particles. This is the basis of the Pauli exclusion principle which forbids two identical fermions to occupy the same quantum state and for example accounts for the ordering of electrons into shells in atoms: the electron has spin 1/2 (and is consequently a fermion) with the two possible spin projections (spin-up) and (spin-down) – hence there can be exactly two in the innermost shell.