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: Spin 1 Particle in a time dependant magnetic field

  1. Dec 7, 2013 #1
    1. The problem statement, all variables and given/known data


    2. Relevant equations

    [tex]\left|\psi ,t\right\rangle=\sum_i c_i(t)e^{-\frac{i E_n t}{\hbar}}\left|n\right\rangle[/tex]

    3. The attempt at a solution

    I'm quite lost on how to even start this. I can work out that the hamiltonian is[tex]H(t)=\gamma S_z B(t)[/tex]Then I tried to put that into the time-dependant shrodinger equation. [tex]-i\hbar \frac{d}{dt}\left|\psi(t)\right\rangle=H(t)\left|\psi(t)\right\rangle[/tex]but I am not really sure if this is correct or even how to begin solving this.
  2. jcsd
  3. Dec 7, 2013 #2


    User Avatar
    Homework Helper
    Gold Member
    2017 Award

    I think you're on the right track. After substituting the given expression for |ψ(t)> into the Schrodinger equation, you should be able to get a differential equation for each coefficient ci(t).
  4. Dec 8, 2013 #3
    I'm still stuck on this one actually. I don't think I am substituting [itex]\left|\psi ,t \right\rangle[/itex] into the equation properly. How to I get [itex]\psi (t)[/itex] from [itex]\left|\psi ,t \right\rangle[/itex]?
  5. Dec 8, 2013 #4
    wait, can I say[tex]\left| \psi ,t \right\rangle=c_1(t)\left| 1,1 \right\rangle+c_2(t)\left| 1,0 \right\rangle+c_3(t)\left| 1,-1 \right\rangle[/tex][tex]\left| \psi ,t \right\rangle=c_1(t)\left(\begin{matrix}1 \\ 0 \\ 0\end{matrix}\right)+c_2(t)\left(\begin{matrix}0 \\ 1 \\ 0\end{matrix}\right)+c_3(t)\left(\begin{matrix}0 \\ 0 \\ 1\end{matrix}\right)[/tex][tex]\left| \psi ,t \right\rangle=\left(\begin{matrix} c_1(t) \\ c_2(t) \\ c_3(t)\end{matrix}\right)[/tex]
  6. Dec 8, 2013 #5
    and then [tex]i\hbar\frac{d}{dt}\left| \psi ,t \right\rangle=\gamma B(t) S_z\left| \psi ,t \right\rangle[/tex]
  7. Dec 8, 2013 #6
    [tex]i\hbar \left(\begin{matrix} c'_1(t) \\ c'_2(t) \\ c'_3(t)\end{matrix}\right)=\hbar\gamma B(t)\left(\begin{matrix}1 & 0&0\\0&0&0\\0&0&-1\\\end{matrix}\right)\left(\begin{matrix} c_1(t) \\ c_2(t) \\ c_3(t)\end{matrix}\right)[/tex]
  8. Dec 8, 2013 #7
    and then get [tex]c'_1(t)=-i\gamma B(t) c_1(t)[/tex][tex]c'_2(t)=0[/tex][tex]c'_3(t)=i\gamma B(t) c_3(t)[/tex]
  9. Dec 8, 2013 #8


    User Avatar
    Homework Helper
    Gold Member
    2017 Award

    Yes, that looks good. Just have to solve each of these equations.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted