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Quantum Mechanics Spin Expectation Value

  1. Oct 31, 2011 #1
    1. The problem statement, all variables and given/known data
    What is the expectation valueof the Sχ for a system in the time-dependent state
    |Ψ> = 2e-2iωt |z+> -ieiωt |z->




    2. Relevant equations
    maybe the state must be normalised first i.e 1/√5 times the initial ψ


    3. The attempt at a solution
    And then say<ψ|Sχ|ψ> where ψ is normalised now and Sx is equal to what ?? .
    Maybe Sx =hbar/2 ψ ??? i think in this very last statement i have to be wrong
     
  2. jcsd
  3. Oct 31, 2011 #2

    dextercioby

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    Who's z+ and z- ? The normalization factor is ok, provided that z+ and z- are normalized.
     
  4. Oct 31, 2011 #3
    We dont know anything more about z 's ,so this part of problem is solved presumably ,most possibly correct.
     
  5. Oct 31, 2011 #4

    vela

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    What do you know about the operator Sx?
     
  6. Oct 31, 2011 #5
    Maybe it can take half integer values ? I really dont know anything else.
     
  7. Oct 31, 2011 #6

    vela

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    Presumably you have a textbook, and it surely covers spin-1/2 systems. Start by reading up on that. Try keeping straight the difference between the operator, its eigenvalues, and its eigenstates. You should be able to calculate what the following equal:
    \begin{align*}
    \hat{S}_x | \uparrow \rangle = \ ? \\
    \hat{S}_x | \downarrow \rangle = \ ?
    \end{align*}where the two states are the eigenstates of Sz.
     
  8. Nov 1, 2011 #7
    the only information i managed to found is that Sx |z+> =hbar/2 |z->

    and Sx|z->=hbar/2|z+>

    but even if we suppose this is correct there is also the problem how to put these in the expression for the expectation value.
     
  9. Nov 1, 2011 #8
    well if this is correct i think i know
     
  10. Nov 1, 2011 #9

    vela

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    That's correct.
     
  11. Nov 1, 2011 #10
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