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The spin magnetic quantum number m s specifies the z-axis component of the spin angular momentum for a particle having spin quantum number s. 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.
s = spin quantum number; m s = spin magnetic quantum number; ℓ = Azimuthal quantum number; m ℓ = azimuthal magnetic quantum number; j = total angular momentum quantum number; m j = total angular momentum magnetic quantum number
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).
The quantum numbers corresponding to these operators are , , (always 1/2 for an electron) and respectively. The energy levels in the hydrogen atom depend only on the principal quantum number n . For a given n , all the states corresponding to ℓ = 0 , … , n − 1 {\displaystyle \ell =0,\ldots ,n-1} have the same energy and are degenerate.
The phrase spin quantum number refers to quantized spin angular momentum. The symbol s is used for the spin quantum number, and m s is described as the spin magnetic quantum number [3] or as the z-component of spin s z. [4] Both the total spin and the z-component of spin are quantized, leading to two quantum numbers spin and spin magnet quantum ...
The photon can be assigned a triplet spin with spin quantum number S = 1. This is similar to, say, the nuclear spin of the 14 N isotope , but with the important difference that the state with M S = 0 is zero, only the states with M S = ±1 are non-zero.
The integer m (not to be confused with the moment, ) is called the magnetic quantum number or the equatorial quantum number, which can take on any of 2j + 1 values: [20], (), , , , +, , + (), + . Due to the angular momentum, the dynamics of a magnetic dipole in a magnetic field differs from that of an electric dipole in an electric field.
The total magnetic moment , as a vector operator, does not lie on the direction of total angular momentum = +, because the g-factors for orbital and spin part are different. However, due to Wigner-Eckart theorem , its expectation value does effectively lie on the direction of J → {\displaystyle {\vec {J}}} which can be employed in the ...