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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 : 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: : 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) : the vector's ''z''-projection is given by : 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）』 ■ウィキペディアで「Total angular momentum quantum number」の詳細全文を読む スポンサード リンク
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