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:
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, and the is the reduced Planck's constant. It ranges from −j to +j in steps of one. This generates 2j + 1 different values of mj.
- 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
- Griffiths, David J. (2004). Introduction to Quantum Mechanics (2nd ed.). Prentice Hall. ISBN 0-13-805326-X.
- Albert Messiah, (1966). Quantum Mechanics (Vols. I & II), English translation from French by G. M. Temmer. North Holland, John Wiley & Sons.