# Precession in the vector model of angular momentum - quantum mechanics?

The vector model of angular momentum in quantum mechanics says that, for example, the angular momentum vector $\mathbf{L}$ precesses about its projection on the $z$ axis, like this:

We can add $\mathbf{L}$ and $\mathbf{S}$ to make $\mathbf{J}$, so that $\mathbf{L}$ and $\mathbf{S}$ precess about $\mathbf{J}$, like this:

NOW:

1) Does the direction of precession (clockwise or anticlockwise) matter?

2) This is just a model, $\mathbf{L}$ and $\mathbf{S}$ do not actually precess, right? So why do use this model? Is it a way to take into account the fact that we don't know $L_x$ and $L_y$?

• 1) the direction does matter (see here). 2) $L$ and $S$ really do precess - it's something we can measure. – lemon Oct 2 '14 at 22:08
• 2) The quantum mechanical operators for L and S do not precess, neither do the states, but their time dependent expectation values do. That's what the model tries to visualize. If you do one measurement, you will always end up with one of the eigenstates. Do the experiment an infinite number of times, average over the result and you will get a precessing vector. Instead of doing the experiment on one spin a large number of times, you can also do it in parallel with a large number of spins. That's what ESR, NMR and optical spin experiments do. – CuriousOne Oct 3 '14 at 2:46