1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Expectation values of spin operators in changing magnetic field

  1. Dec 25, 2012 #1
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
    I have totally no idea how to solve this question. But I find it somehow similar to the Larmor precession problem. Therefore I try to solve my problem by referring to that.
    Are there any mistakes if I do it like this?

    p.s. since the matrix elements are quite complicated, in order to save time, I use "c" to stand for cosine, "e" to stand for exponential that repeat over and over again.

    Attached Files:

  2. jcsd
  3. Dec 26, 2012 #2


    User Avatar
    Homework Helper
    Gold Member
    2017 Award

    It looks like you're taking the spin state of the particle at time t = 0 to be proportional to ##\left(\begin{array}{c}1\\0\end{array}\right)##. That would correspond to spin up along the z-axis. But at t = 0 the spin state is an eigenstate of the Hamiltonian H for a magnetic field in the direction specified by ##\theta## and ##\phi##. In particular, it's the state that corresponds to "spin up" along the ##\theta##, ##\phi## direction (or, positive energy eigenvalue for H).
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook