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

Total Angular Momentum

The total angular momentum is the vector sum of the spin angular momentum S and orbital angular momentum L,

(1)

It is quantized by two quantum numbers j and as

(2)

(3)

Here, j is the first total angular momentum quantum number, which takes half-integer values given by

(4)

with l the azimuthal quantum number. Similarly, is the second total angular momentum quantum number, which takes half-integer values given by , ..., j.

Azimuthal Quantum Number, Orbital Angular Momentum, Spin Angular Momentum, Total Angular Momentum Quantum Numbers

References

Arfken, G. Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 186-187, 1985.

Eisberg, R. and Resnick, R. "Total Angular Momentum." §8-5 in Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles, 2nd ed. New York: Wiley, pp. 281-284, 1985.

Gasiorowicz, S. Quantum Physics. New York: Wiley, 1974.

Rose, M. E. Elementary Theory of Angular Momentum. New York: Dover, 1995.

Varshalovich, D. A.; Moskalev, A. N.; and Khersonskii, V. K. "Total Angular Momentum Operator." §2.1 in Quantum Theory of Angular Momentum. Singapore: World Scientific, pp. 36-39, 1988.