orbeckst
commented
8 years ago I am not sure I follow entirely. It would help if you wrote down the equations of motions that you want to solve together with the model for the magnetic moment.
The classical model simply says that the "spin" is a vector that can take on any orientation.
Quantum mechanics says that you cannot really talk about a vector (Sx,Sy,Sz) because the three operators do not commute and you cannot know where the tip of vector is; all you know is the length of the vector and one projection (eg Sz, because [S^2, Sz] = 0. The way to model this semiclassically is a rotating vector (with Larmor frequency) with constant z component.
Some more general comments:
You could start out with a purely classical simulation where the magnetic moment of the silver atoms can have any direction. Your beam then simply draws from a random distribution of orientations (for the sphere this is actually a bit involved, as shown in Sphere Point Picking from MathWorld – although if you have a method to generate Gaussian random variables (check scipy or numpy.random!) then it's easy, see bottom of the linked page.
Then do the semi-classical calculation where the only allowed magnetic moments have z-component ±1/2 * µB (and where the vector precesses with the Larmor frequency).
Finally, it would be neat to solve the time dependent Schrödinger equation for a wave packet with spin.
@andrewdurkiewicz said: My group and I are having an issue with our project. I cant seem to get through the boundaries for spin in different axis for the classical model. We began our project forcing S_z to be within -1/2 and 1/2. But the issue is that since S^2 = 3/4 = s_x^2 + s_y^2 + s_z^2 . We know that in quantum, S_z = +/- 1/2 , but for our project we took the classical model as saying that s_z must be bounded as : -1/2 <= S_z <= 1/2 . We say this because the direction of the spin can be up,down, forward, back, etc as it passes through the magnetic field. In classical there is no reason to presume it cannot have a spin perpendicular to the magnetic field in the x/y direction. This causes a huge issue. It means that if I align the spin in the x , y , z , then we get a contradiction. this is because we get that 1/4 = 3/4. The reason that I am emailing you is that we are deeply confused on how to approach this. What I want to do instead is say that the 3/4 is purely quantum mechanical, and think about this as quantum mechanics wasn't really a thing yet. To me, this means that the spin-space-sphere has a radius of 1. And 1 = S_x^2 + S_y^2 + S_z^2. But would this make it a boson? Any advice would be appreciated. We are considerably confused on this.
Note, when I say classical, I mean semi-classical/quantum.