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In the Bohr model of the atom, for an electron that is in the orbit of lowest energy, its orbital angular momentum has magnitude equal to the reduced Planck constant, denoted ħ. The Bohr magneton is the magnitude of the magnetic dipole moment of an electron orbiting an atom with this angular momentum. [14]
The operator on the left represents the particle energy reduced by its rest energy, which is just the classical energy, so we recover Pauli's theory if we identify his 2-spinor with the top components of the Dirac spinor in the non-relativistic approximation. A further approximation gives the Schrödinger equation as the limit of the Pauli ...
The magnetic moment of the electron is =, where μ B is the Bohr magneton, S is electron spin, and the g-factor g S is 2 according to Dirac's theory, but due to quantum electrodynamic effects it is slightly larger in reality: 2.002 319 304 36.
The best available measurement for the value of the magnetic moment of the neutron is μ n = −1.913 042 76 (45) μ N. [3] [4] Here, μ N is the nuclear magneton, a standard unit for the magnetic moments of nuclear components, and μ B is the Bohr magneton, both being physical constants.
In the first-order Zeeman effect the energy difference between the two states is proportional to the applied field strength. Denoting the energy difference as Δ E , the Boltzmann distribution gives the ratio of the two populations as e − Δ E / k T {\displaystyle e^{-\Delta E/kT}} , where k is the Boltzmann constant and T is the temperature ...
The above classical relation does not hold, giving the wrong result by the absolute value of the electron's g-factor, which is denoted g e: = | | =, where μ B is the Bohr magneton. The gyromagnetic ratio due to electron spin is twice that due to the orbiting of an electron.
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).
Continuous charge distribution. The volume charge density ρ is the amount of charge per unit volume (cube), surface charge density σ is amount per unit surface area (circle) with outward unit normal n̂, d is the dipole moment between two point charges, the volume density of these is the polarization density P.