Total Angular Momentum Quantum Numbers -- from Eric Weisstein's World of Physics

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Total Angular Momentum Quantum Numbers

The total angular momentum J is quantized by two quantum numbers, j and . These are related to the magnitude and z-component of J through

j can take on only half-integer values

where l = 0, 1, ..., is the azimuthal quantum number, and can take on only the half-integer values , ..., j.

Azimuthal Quantum Number, Total Angular Momentum