Precessing electron, probability of spins

[joex444]

Homework Statement

An electron precesses in B field aligned with +z axis. At t=0, spin of the electron is in the +x direction. Wave function is given as a matrix, but is equal to 1/sqrt(2)[e^-iwt/2 |z> + e^iwt/2 |-z> ]. (Sorry, idk LaTeX). For t>0, find the probability of finding the electron in the state:

(a) ms = +h/2 [h-bar] [m sub s]
(b) msx = +h/2 [h-bar] [m sub sx]

Homework Equations

The Attempt at a Solution

Actually, I just want to make sure I set these problem up right. I have the answers, and I did get the correct answers, but:

for (a): I did |<z|psi>|^2, it came out to 1/2
for (b): I did |<x|psi>|^2, it came out to cos^2(wt/2)

I'm not sure if my setup for (a) was right, or not. I could've got the same result with |<-z|psi>|^2, for example. I'm not sure if its a notation thing with the book, they tend to use msx and msy, but I don't recall seeing msz, perhaps they use the notation that msz = ms. This makes some sense, as there is no such thing as definite total spin, even with just 1 electron.

 

[Jhero]

Thank you for your question. Your setup for part (a) is correct. The notation used in the book may be a bit confusing, but in this case, msz does refer to the z-component of the spin, which is equal to ms. So you were correct to use |<z|psi>|^2 for part (a).

For part (b), your approach is also correct. The notation msx may refer to the x-component of the spin, so using |<x|psi>|^2 is the appropriate approach.

Overall, it seems like you have a good understanding of the problem and your solutions are correct. Keep up the good work!