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Given the initial state, Ican find the time evolution wave function right?

  1. Oct 27, 2007 #1

    cks

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    1. The problem statement, all variables and given/known data
    At t=0, the particle is in the eigenstate [tex] S_x [/tex], which corresponds to the eigenvalues [tex] -\hbar \over 2 [/tex]The particle is in a magnetic field and its Hamiltonian is [tex] H=\frac{eB}{mc}S_z [/tex]. Find the state at t>0.


    2. Relevant equations

    Eigenstate of the Sx is

    [tex] |->_x=\frac{1}{2^\frac{1}{2}}(|+>-|->) [/tex]



    3. The attempt at a solution

    Since I am given with the initial state, then

    [tex] |-(t)>_x=\frac{1}{2^\frac{1}{2}}(e^\frac{-iE_+t}{\hbar}|+>-e^\frac{-iE_-t}{\hbar}|->) [/tex]

    where [tex] E_t=\frac{eB}{mc} [/tex]

    and [tex] E_-=-\frac{eB}{mc} [/tex]

    Why am I wrong?
     
  2. jcsd
  3. Oct 27, 2007 #2

    nrqed

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    Looks right to me except for a factor of hbar/2 missing in your energies.
     
  4. Oct 28, 2007 #3

    cks

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    yaya, aisheah, thank you very much. why I always miss something!!!
     
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