Question

What is the significance of spin? How does it affect the wave function? I just need help putting this into place in my brain.

I know that spin is a result of the intrinsic angular momentum of a charged particle that causes it to have a magnetic field and thus be affected by weak external magnetic fields. I think I understand the Stern-Gerlach experiment, but I don't understand how it applies to the wave function for particles in a box. Does it?

Answer 1

You can think of the spin as an additional discrete degree of freedom of a particle.

You might find some help here
http://en.wikipedia.org/wiki/Wave_function
in the section 'Definitions (other cases)'

Answer 2

Thank you! :)

Answer 3

It seems like we're not going that much into detail with spin in my class. Rather, we recognize it as an intrinsic property of a (I think) charged particle. We use it to find the total angular momentum and we acknowledged that it allows two electrons to be at the same energy in a system with differing spin.

Take care!

Answer 4

I think I have something to add here, just for others' reference. But anyone correct me if I'm wrong!

With indistinguishable particles, we have to create a wave function that will account for either particle in either wave function. There are two expressions to capture this, one is symmetric and the other is antisymmetric. Spin-\(\frac12\) particles are theoretically and experimentally shown to follow the antisymmetric probability distribution, I think. This actually leads to the exclusion principle, and explains why it applies only to that antisymmetric distribution that is for fermions.

So there's a big relevance for spin in the wave function.

Answer 5

Yes, integral spin particles (bosons) have symmetric wavefunctions and half odd integral spin particles (fermions) have antisymmetric wavefunctions (with respect to exchange of particles, that is)
It's known as the spin-statistics theorem, I think.
Richard Feynman commented somewhere that no one can give a simple explanation of why it is that way, so we don't really understand it.

Answer 6

Haha, I look forward to learning more and continuing to not understand, then!! Thank you!