Spin quantum number
In atomic physics, the spin quantum number is a quantum number that parameterizes the intrinsic angular momentum (or spin angular momentum, or simply spin) of a given particle. The spin quantum number is the fourth of a set of quantum numbers (the principal quantum number, the azimuthal quantum number, the magnetic quantum number, and the spin quantum number), which completely describe the quantum state of an electron. It is designated by the letter s. It describes the energy, shape and orientation of orbitals.
As a solution for a certain partial differential equation, the quantized angular momentum (see angular momentum quantum number) can be written as:
where
Given an arbitrary direction z (usually determined by an external magnetic field) the spin z-projection is given by
where ms is the secondary spin quantum number, ranging from −s to +s in steps of one. This generates 2 s + 1 different values of ms.
The allowed values for s are non-negative integers or half-integers. Fermions (such as the electron, proton or neutron) have half-integer values, whereas bosons (e.g., photon, mesons) have integer spin values.
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