Angular Momentum

[snow5379]

Angular momentum is a conserved thing (I think?). So... what happens when an electron (spin 0.5) absorbs a photon (spin 1)? Does the electron now have a spin of 1.5? Does it spin faster? What if the electron has a spin of -0.5? I'm referring to a free electron by the way.

Also I'm sorry for asking so many questions... I've taken a liking to physics recently and it seems for every thing I learn a dozen more questions arise.

If a free electron can't absorb a photon what happens to the angular momentum of each when a photon bounces off an electron? Is it left untouched?

[yurell]

Angular momentum is a conserved property. However, a free electron can't absorb a photon.

[mfb]

It can absorb and re-emit a photon (compton effect). But this is not what you are looking for, right?

And keep in mind that angular momentum is not just spin.

[LaserGuy]

Angular momentum is a conserved thing (I think?). So... what happens when an electron (spin 0.5) absorbs a photon (spin 1)? Does the electron now have a spin of 1.5? Does it spin faster? What if the electron has a spin of -0.5? I'm referring to a free electron by the way.

Also I'm sorry for asking so many questions... I've taken a liking to physics recently and it seems for every thing I learn a dozen more questions arise.

If a free electron can't absorb a photon what happens to the angular momentum of each when a photon bounces off an electron? Is it left untouched?

Spin in quantum mechanics does not mean "spin" like you would normally think of it for a real object. Although the mathematics do behave similarly, it is not correct to say that something in a spin state of 1 is spinning "faster" than a spin state of 1/2. This quantity does not have a good macroscopic analogue--the choice of the word "spin" is mostly historical--because nothing, as far as we can tell, as actually spinning.

You have to be a bit careful when adding spins. When we say an electron has spin of 1/2, it can take values of +1/2 or -1/2. A spin 1 photon can take values of +1, 0, or -1. All other values simply cannot exist. So if an electron with +1/2 spin were to scatter off a photon with 0 spin, then either the electron would remain at +1/2 and the photon would remain at 0, or the electron would switch to -1/2 and the photon would switch to +1.

[snow5379]

Actually that's exactly what I was looking for! Thanks. With that effect no angular momentum is transferred though right?

EDIT

So... bouncing a photon off an electron could reverse the spins of each?

[yurell]

I was under the impression that photons always carried angular momentum (hence why it takes so long for an atom to transition from a 0+ state to another 0+ state)?

Quick Google double-check says photons always have spin angular momentum of ±ħ

[snow5379]

I'm pretty sure photons always have angular momentum of +hbar or -hbar and can't have an angular momentum of 0.

I'm wondering now though if a photon striking an electron could cause the photons spin to change from, say, +hbar to -hbar or the electron's spin to change from +hbar/2 ro -hbar/2.

[yurell]

The easiest way to show that a free electron cannot absorb a photon is conservation of momentum energy.

Write down P_before (best to choose it in the electron's rest frame) and P_after.
Write down E_before and E_after.
Equate the two using E²=P²c² + m²c⁴.

You should find the only solution is the electron moving faster than light as far as I can recall (don't have time before class to run the calculation myself).

Edit: I don't think the photon can flip the free electron's spin and maintain conservation of angular momentum, since the electron gains one unit of angular momentum while the photon loses two, and we can pick point from which they're both retreating radially (and thus have no other angular momentum w.r.t. it).

[mfb]

I'm pretty sure photons always have angular momentum of +hbar or -hbar and can't have an angular momentum of 0.

In the direction of movement, or in other directions?
Space is 3-dimensional (well, 4 with time), so the system is a bit more complicated.

[Charlie!]

I'm pretty sure photons always have angular momentum of +hbar or -hbar and can't have an angular momentum of 0.

In the direction of movement, or in other directions?
Space is 3-dimensional (well, 4 with time), so the system is a bit more complicated.

Hmm, interesting puzzle. The photon must always have a spin of +-1 in the direction of motion (since it's gotta be a transverse wave). If we call the direction of motion the x-direction, what does that look like from the z-direction? Well, it looks like the +1 and -1 eigenvectors of the spin-1 X pauli matrix, which maps the middle to the outsides and the outsides to the middle. This is solved by (1/sqrt(2), +-1, 1/sqrt(2)), which does have half its probability mass in the spin-0 state. So if you emit a linearly polarized photon in the x-direction you can keep the z-direction spin of your atom the same.

[LaserGuy]

I'm pretty sure photons always have angular momentum of +hbar or -hbar and can't have an angular momentum of 0.

I'm wondering now though if a photon striking an electron could cause the photons spin to change from, say, +hbar to -hbar or the electron's spin to change from +hbar/2 ro -hbar/2.

If the photon has to have spin +/-1, then I think the answer would be have to be no. There's no way to make the transition and have angular momentum between the particles conserved, because the spin on the photon has to change by two, and the electron can only change by one.

[Minerva]

An electron can't "absorb" a photon. It might couple to a photon, sure.

Also, +1 to previous comments - "spin" is really just a quantum number with a funny name, like strangeness or charm or truth or beauty. It's entirely a quantum-mechanical thing which needs to be learned and understood entirely in terms of QM.

It's not something "spinning" like anything in classical mechanics - although it just kind of behaves mathematically similarly to an angular momentum.

[SU3SU2U1]

Also, +1 to previous comments - "spin" is really just a quantum number with a funny name, like strangeness or charm or truth or beauty

Well, it IS angular momentum, its not something totally independent from classical mechanics (like quark flavor). Instead of spin, "intrinsic angular momentum" might be a more descriptive name. Its important to remember that while spin isn't individually conserved, total angular momentum is.

I think the best classical analogue for spin might be the field-angular momentum in electricity and magnetism. The field isn't "spinning" but it does have angular momentum.

[PM 2Ring]

As I said here:

QM spin is different to what we're used to in the macroscopic world, but you can say the same thing about position, linear momentum and energy; things tend to be somewhat counter-intuitive in their quantized form. It's just that QM spin is even more counter-intuitive because in the macroscopic world we have no experience of intrinsic angular momentum, only orbital angular momentum.

An object like a spinning top (or a spinning planet) is composed of a bunch of particles that are rotating around a common central axis, so all those particles have orbital angular momentum. So it's natural that when we think of something having spin to think in terms of a collection of parts that have orbital angular momentum around some axis. In the quantum world, a particle like an electron or a photon has no parts, so that model cannot apply. But that doesn't mean that they aren't really spinning.