# What is total angular momentum: Definition and 64 Discussions

In quantum mechanics, the total angular momentum quantum number parametrises 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, and the

{\displaystyle \hbar }
is the reduced Planck's constant. It ranges from −j to +j in steps of one. This generates 2j + 1 different values of mj.
The total angular momentum corresponds to the Casimir invariant of the Lie algebra so(3) of the three-dimensional rotation group.

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3. ### I Total angular momentum of a translating and rotating pancake

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4. ### B Falling Cat - Rotation with Zero Total Angular Momentum

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20. ### Total angular momentum operators

Sometimes the concept of angular momentum is presented using the idea of total angular momentum J. In those cases, its always said that we have \vec{J}=\vec L + \vec S . But I can't understand how that's possible. Because orbital angular momentum operators are differential operators and so are...
21. ### Eigen value of total angular momentum

I'm trying to understand why the eigen value of the total angular momentum L^{2} is \hbar ^2 l(l+1). The proofs I have seen go like this. Using the ladder operators L_{\pm} = L_x \pm iL_y we can see and the |l, m \rangle state with maximum value of m (eigen value of L_z ) \langle l,m_{max} |...
22. ### Total angular momentum of atom in its ground state

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23. ### Total Angular Momentum and Binding Energy

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24. ### Spin,orbital and total angular momentum

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25. ### LS coupling and calculating the total angular momentum

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26. ### Total Angular Momentum of Circularly Polarised Light

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27. ### Total Angular Momentum Commutation Relations for 2 Particle

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28. ### Uncertainties & Total Angular Momentum

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29. ### Possible values of total angular momentum of a 2 electron system

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30. ### Eigenvalue of Total Angular Momentum Probability

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31. ### [QM] Total angular momentum rotation operator

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32. ### Total angular momentum OP

HI,i am aiming to show that 1/(2)^1/2(|spin up>|spin down> + |spin down>|spin up>) is an eigenvalue to the total angular momentum operator in a two-electron system. I know that i should end up with getting the eigenvalues of the separate spins; L1|spin up> and L2|spin down> and so...
33. ### Lande g-factor and total angular momentum conservation

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34. ### Finding total angular momentum qnumber for 3d4d

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35. ### Why Does Electron Angular Momentum Not Align with External Field?

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36. ### Total Angular Momentum in Nuclear Shell Model

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37. ### Dimensionality of total angular momentum space

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38. ### Total Angular Momentum of 2 connected falling bodies.

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39. ### Is the space of total angular momentum complete?

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40. ### Larmor Frequency spin, orbital or total angular momentum?

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41. ### Total angular momentum of Positronium

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42. ### What are the total angular momentum states for l = 3, s = ½?

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43. ### Total angular momentum of a sphere that had both a linear v and an angular v?

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44. ### Possible Values for Total Angular Momentum

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45. ### Total Angular Momentum of A System

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46. ### Total Angular Momentum of the Earth

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47. ### Calculating Angular Momentum for a Rolling Sphere

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48. ### Total Angular Momentum of Two Nucleons: Possible Values?

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49. ### [qm]find the angular opertor given total angular momentum wavefunction

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50. ### What's the total angular momentum operator for a system of two particles?

Suppose we're in two dimensions, and both particles have mass 1. Particle 1's location is given by its polar coordinates (r_1,\theta_1); likewise for Particle 2 (r_2,\theta_2). Is it true that the total angular momentum \vec{L} is just the sum of the individual angular momenta of the...