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The conventional definition of the spin quantum number is s = n / 2 , where n can be any non-negative integer. Hence the allowed values of s are 0, 1 / 2 , 1, 3 / 2 , 2, etc. The value of s for an elementary particle depends only on the type of particle and cannot be altered in any known way (in contrast to the spin ...
The (total) spin quantum number has only one value for every elementary particle. Some introductory chemistry textbooks describe m s as the spin quantum number, [6] [7] and s is not mentioned since its value 1 / 2 is a fixed property of the electron; some even use the variable s in place of m s. [5]
The spin representation Δ further decomposes into a pair of irreducible complex representations of the Spin group [26] (the half-spin representations, or Weyl spinors) via + =, =. When dim( V ) is odd, V = W ⊕ U ⊕ W ′ , where U is spanned by a unit vector u orthogonal to W .
Spin is the fundamental property that distinguishes the two types of elementary particles: fermions, with half-integer spins; and bosons, with integer spins. Photons, which are the quanta of light, have been long recognized as spin-1 gauge bosons. The polarization of the light is commonly accepted as its “intrinsic” spin degree of freedom ...
S is the total spin quantum number for the atom's electrons. The value 2S + 1 written in the term symbol is the spin multiplicity, which is the number of possible values of the spin magnetic quantum number M S for a given spin S. J is the total angular momentum quantum number for the atom's electrons. J has a value in the range from |L − S ...
This is the continuous spin representation. In d + 1 dimensions, the little group is the double cover of SE( d − 1 ) (the case where d ≤ 2 is more complicated because of anyons , etc.). As before, there are unitary representations which don't transform under the SE( d − 1 ) "translations" (the "standard" representations) and "continuous ...
Spin- 1 / 2 particles can have a permanent magnetic moment along the direction of their spin, and this magnetic moment gives rise to electromagnetic interactions that depend on the spin. One such effect that was important in the discovery of spin is the Zeeman effect , the splitting of a spectral line into several components in the ...
The spin magnetic moment of the electron is =, where is the spin (or intrinsic angular-momentum) vector, is the Bohr magneton, and = is the electron-spin g-factor. Here μ {\displaystyle {\boldsymbol {\mu }}} is a negative constant multiplied by the spin , so the spin magnetic moment is antiparallel to the spin.