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Heuristic depiction of spin angular momentum cones for a spin- 1 / 2 particle. Spin- 1 / 2 objects are all fermions (a fact explained by the spin–statistics theorem) and satisfy the Pauli exclusion principle. Spin- 1 / 2 particles can have a permanent magnetic moment along the direction of their spin, and this magnetic ...
The number "2s + 1" is the multiplicity of the spin system. For example, there are only two possible values for a spin- 1 / 2 particle: s z = + 1 / 2 and s z = − 1 / 2 . These correspond to quantum states in which the spin component is pointing in the +z or −z directions respectively, and are often referred to as "spin ...
The atom would then be pulled toward or away from the stronger magnetic field a specific amount, depending on the value of the valence electron's spin. When the spin of the electron is + + 1 / 2 the atom moves away from the stronger field, and when the spin is − + 1 / 2 the atom moves toward it. Thus the beam of silver atoms is ...
Here, 1 / 2 σ μν and F μν stand for the Lorentz group generators in the Dirac space, and the electromagnetic tensor respectively, while A μ is the electromagnetic four-potential. An example for such a particle [9] is the spin 1 / 2 companion to spin 3 / 2 in the D (½,1) ⊕ D (1,½) representation space of the ...
In quantum mechanics, a triplet state, or spin triplet, is the quantum state of an object such as an electron, atom, or molecule, having a quantum spin S = 1. It has three allowed values of the spin's projection along a given axis m S = −1, 0, or +1, giving the name "triplet". Spin, in the context of quantum mechanics, is not a mechanical ...
Fermions have a half-integer spin (spin 1 / 2 , spin 3 / 2 , etc.) and obey the Pauli exclusion principle. These particles include all quarks and leptons and all composite particles made of an odd number of these, such as all baryons and many atoms and nuclei. Fermions differ from bosons, which obey Bose–Einstein statistics.
Atoms can have different overall spin, which determines whether they are fermions or bosons: for example, helium-3 has spin 1/2 and is therefore a fermion, whereas helium-4 has spin 0 and is a boson. [ 2 ] : 123–125 The Pauli exclusion principle underpins many properties of everyday matter, from its large-scale stability to the chemical ...
For an electron, s is 1 ⁄ 2, and m s is either + 1 ⁄ 2 or − 1 ⁄ 2, often called "spin-up" and "spin-down", or α and β. [1] [2] The term magnetic in the name refers to the magnetic dipole moment associated with each type of angular momentum, so states having different magnetic quantum numbers shift in energy in a magnetic field ...