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Total angular momentum quantum number : ウィキペディア英語版
Total angular momentum quantum number

In quantum mechanics, the total angular momentum quantum number parameterises the total angular momentum of a given particle, by combining its orbital angular momentum and its intrinsic angular momentum (i.e., its spin).
If s is the particle's spin angular momentum and ℓ its orbital angular momentum vector, the total angular momentum j is
:\mathbf j = \mathbf s + \boldsymbol
The associated quantum number is the main total angular momentum quantum number ''j''. It can take the following range of values, jumping only in integer steps:
:|\ell - s| \le j \le \ell + s
where ''ℓ'' is the azimuthal quantum number (parameterizing the orbital angular momentum) and ''s'' is the spin quantum number (parameterizing the spin).
The relation between the total angular momentum vector j and the total angular momentum quantum number ''j'' is given by the usual relation (see angular momentum quantum number)
: \Vert \mathbf j \Vert = \sqrt \, \hbar
the vector's ''z''-projection is given by
:j_z = m_j \, \hbar
where ''mj'' is the secondary total angular momentum quantum number. It ranges from −''j'' to +''j'' in steps of one. This generates 2''j'' + 1 different values of ''m''''j''.
The total angular momentum corresponds to the Casimir invariant of the Lie algebra so(3) of the three-dimensional rotation group.
==See also==

* Principal quantum number
* Orbital angular momentum quantum number
* Magnetic quantum number
* Spin quantum number
* Angular momentum coupling
* Clebsch–Gordan coefficients
* Angular momentum diagrams (quantum mechanics)
* Rotational spectroscopy

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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