text: The<unk>  is one of the most important<unk> s in physics, primarily because the three types of particles from which ordinary matter is made—electrons, protons, and neutrons—are all subject to it; consequently, all material particles exhibit space-occupying behavior. The<unk>  underpins many of the characteristic properties of matter from the large-scale stability of matter to the existence of the periodic table of the elements.
  The<unk>  follows mathematically from the definition of the angular momentum operator (rotation operator) in quantum mechanics.  The exchange of particles in the system of two identical particles (which is mathematically equivalent to the rotation of each particle by 180 degrees) results either in the change of the sign of wave function of the system (when the particles have half-integer spin) or not (when the particles have integer spin). Thus, no two identical particles of half integer spin can be at the same quantum place - because the wave function of such system must be equal to its opposite - and the only wave function which satisfies this condition is the zero wave function.
  Particles with antisymmetric wave functions are called fermions—and obey the<unk> . Apart from the familiar electron, proton and neutron, these include neutrinos and quarks (from which protons and neutrons are made), as well as some atoms like helium-3. All fermions possess "half-integer spin", meaning that they possess an intrinsic angular momentum whose value is 
  ℏ
  =
  h
  /
  2
  π
  {\displaystyle \hbar =h/2\pi }
   (Planck's constant divided by 2π) times a half-integer (1/2, 3/2, 5/2, etc.). In the theory of quantum mechanics, fermions are described by "antisymmetric states", which are explained in greater detail in the article on identical particles.
  Particles with integer spin have a symmetric wave function and are called bosons; in contrast to fermions, they may share the same quantum states. Examples of bosons include the photon and the W and Z bosons.
option_0: Pauli exclusion principle
option_1: Fukuyama coupling
option_2: Franck-Condon principle
option_3: Accessory pathway
option_4: Behrens-Fisher problem
option_5: Weber–Fechner law
option_6: D-dimer physiology
option_7: Pulsatile flow