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Perfect Gases
Published in Jeffrey Olafsen, Sturge’s Statistical and Thermal Physics, 2019
We know from quantum mechanics that there are two general classes of particles: fermions and bosons. A fermion has odd half-integer spin,2 its many-particle wave functions are anti-symmetric, and because of this anti-symmetry, it obeys the Pauli principle that only one particle can occupy a given single particle state; that is, n = 0 or 1. Examples of fermions are the electron, neutrino, muon, proton, neutron, quark, and all nuclei with odd mass numbers(e.g., 3He). A boson has zero or integer spin and has symmetric many-particle wave functions, so that any number of bosons can occupy the same single particle state; that is, n can have any non-negative value. Examples are the photon (γ), pion (π+), gluon (g), and any nucleus with even mass number (e.g., the deuteron 2 H and the alpha particle 4He). We must deal with fermions and bosons separately, since their statistics are very different.
Interlude of Physics I: Quantum Mechanics
Published in Franco Battaglia, Thomas F. George, Understanding Molecules, 2018
Franco Battaglia, Thomas F. George
A particle wavefunction shall still be denoted as Ψ(r,t), but now the argument r denotes all four variables: the three position space components (which, if Cartesian, may each take all real values) and the spin component, msħ (where ms may take 2s + 1 discrete values from −s to s with integer steps of unity). Alternatively, we could denote it as Ψms = Ψms(r,t) (in this case r represents the space components only). Whatever the notation, the integrals appearing in the fundamental postulate, Eq. (4.25), and in the relations derived from it (such as the normalization to unity of the wavefunction) have to be considered as integrals over the space components and sum over the spin components. Particles with integer spin are called bosons, and those with half-integer spin are called fermions. Protons, neutrons, and electrons all have spin quantum number s = 1/2, and thus are fermions.
Electrons and anti-symmetry
Published in David K Ferry, Quantum Mechanics, 2001
Now, what do we really mean by bosons and fermions? In the previous paragraph, we stated that bosons do not obey the Pauli exclusion principle, and do obey the Bose–Einstein distribution. On the other hand, fermions do obey the Pauli exclusion principle–no more than two fermions, and these are of opposite spin—can be accomodated in any quantum state. Bosons are particles with integer spin, such as phonons (zero spin) and photons (integer spin given by ±1, corresponding to right- and left-circularly polarized plane waves for example). Fermions are particles with half-integer spin, such as electrons. These two distributions are given by () fBE(E)=1eE/kBT-1
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.