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- https://phys.libretexts.org/Learning_Objects/A_Physics_Formulary/Physics/10%3A_Quantum_PhysicsQuantum mechanics, atomic physics, Schrödinger and Dirac equations
- https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Quantum_Mechanics_III_(Chong)/04%3A_Identical_Particles/4.02%3A_Symmetric_and_Antisymmetric_StatesHence, Equation (???) is explicitly symmetric: \[\begin{align} \begin{aligned} \hat{P}_{12} \, |+\!z, A\,;\, -z, B\rangle &= \frac{1}{\sqrt{2}} \Big(|\!-\!z\rangle|B\rangle |\!+\!z\rangle|...Hence, Equation (???) is explicitly symmetric: ˆP12|+z,A;−z,B⟩=1√2(|−z⟩|B⟩|+z⟩|A⟩+|+z⟩|A⟩|−z⟩|B⟩)=|+z,A;−z,B⟩. Likewise, if there is a spin-down particle at A and a spin-up particle at B, the bosonic two-particle state is \[|-\!z, A\,;\, +z, B\rangle = \frac{1}{\sqrt{2}} \Big…
- https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Quantum_Mechanics_(Fowler)/05%3A_Interlude_-_The_Nature_of_Electrons/5.01%3A_Bosons_and_FermionsSo far, we have used Schrödinger’s equation to see how a single particle, usually an electron, behaves in a variety of potentials. If we are going to think about atoms other than hydrogen, it is neces...So far, we have used Schrödinger’s equation to see how a single particle, usually an electron, behaves in a variety of potentials. If we are going to think about atoms other than hydrogen, it is necessary to extend the Schrödinger equation so that it describes more than one particle. All elementary particles are either fermions, which have antisymmetric multiparticle wavefunctions, or bosons, which have symmetric wave functions. Electrons, protons and neutrons are fermions; photons are bosons.
- https://phys.libretexts.org/Courses/Georgia_State_University/GSU-TM-Introductory_Physics_II_(1112)/zz%3A_Back_Matter/10%3A_13.1%3A_Appendix_J-_Physics_Formulas_(Wevers)/1.10%3A_Quantum_PhysicsQuantum mechanics, atomic physics, Schrödinger and Dirac equations
- https://phys.libretexts.org/Bookshelves/University_Physics/Radically_Modern_Introductory_Physics_Text_II_(Raymond)/19%3A_Atoms/19.01%3A_Fermions_and_BosonsIn this case the probability of finding particle 1 at x1 and particle 2 at x2 is just the absolute square of the joint wave amplitude: \(\mathrm{P}\left(\mathrm{x}_{1},...In this case the probability of finding particle 1 at x1 and particle 2 at x2 is just the absolute square of the joint wave amplitude: P(x1,x2)=P1(x1)P2(x2).
- https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Introductory_Quantum_Mechanics_(Fitzpatrick)/05%3A_Multi-Particle_Systems/5.04%3A_Identical_ParticlesWavefunctions of systems containing many identical particles are symmetric or anti-symmetric under interchange of the labels on any two particles is determined by the nature of the particles themselve...Wavefunctions of systems containing many identical particles are symmetric or anti-symmetric under interchange of the labels on any two particles is determined by the nature of the particles themselves . Wavefunctions that are symmetric under label interchange are said to obey Bose-Einstein statistics , and are called bosons. For instance, photons are bosons. Wavefunctions that are anti-symmetric under label interchange are said to obey Fermi-Dirac statistics , and are called fermions.
