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Since m 0 does not change from frame to frame, the energy–momentum relation is used in relativistic mechanics and particle physics calculations, as energy and momentum are given in a particle's rest frame (that is, E ′ and p ′ as an observer moving with the particle would conclude to be) and measured in the lab frame (i.e. E and p as ...
Spin is an intrinsic form of angular momentum carried by elementary particles, and thus by composite particles such as hadrons, atomic nuclei, and atoms. [1] [2]: 183–184 Spin is quantized, and accurate models for the interaction with spin require relativistic quantum mechanics or quantum field theory.
Crystal momentum also earns its chance to shine in these types of calculations, for, in order to calculate an electron's trajectory of motion using the above equations, one need only consider external fields, while attempting the calculation from a set of equations of motion based on true momentum would require taking into account individual ...
In physics and chemistry, the spin quantum number is a quantum number (designated s) that describes the intrinsic angular momentum (or spin angular momentum, or simply spin) of an electron or other particle. It has the same value for all particles of the same type, such as s = 1 / 2 for all electrons.
For example, an electron and a positron, each with a mass of 0.511 MeV/c 2, can annihilate to yield 1.022 MeV of energy. A proton has a mass of 0.938 GeV/c 2. In general, the masses of all hadrons are of the order of 1 GeV/c 2, which makes the GeV/c 2 a convenient unit of mass for particle physics: [4]
The spin magnetic moment of a charged, spin-1/2 particle that does not possess any internal structure (a Dirac particle) is given by [1] =, where μ is the spin magnetic moment of the particle, g is the g-factor of the particle, e is the elementary charge, m is the mass of the particle, and S is the spin angular momentum of the particle (with magnitude ħ/2 for Dirac particles).
In atomic physics, the electron magnetic moment, or more specifically the electron magnetic dipole moment, is the magnetic moment of an electron resulting from its intrinsic properties of spin and electric charge. The value of the electron magnetic moment (symbol μ e) is −9.284 764 6917 (29) × 10 −24 J⋅T −1. [1]
Here, J is the total electronic angular momentum, L is the orbital angular momentum, and S is the spin angular momentum. Because = / for electrons, one often sees this formula written with 3/4 in place of (+). The quantities g L and g S are other g-factors of an electron.