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Quantum Mechanics expectation value problem

  1. Oct 18, 2009 #1
    1. The problem statement, all variables and given/known data

    An electron is in the spin state in the Sz representation

    |ψ> = A (1-2i 2)T <- this is a 2 X 1 matrix

    If Sx is measured, what values and probabilities do you get?
    What is the expectation value of Sx?


    2. Relevant equations


    3. The attempt at a solution

    So first, I need to find what A equals to:

    A^2 [ (1-2i)(1+2i)+ 4 ] = 1
    thus A = 1/3

    now, I need to know what values of Sx I would get and the probabilities to
    proceed to find the expectation value.

    What values of Sx would I get??? could it be just +/- h-bar/2 ??
    What would be the probabilities??

    I would really appreciate any hint or help!
     
  2. jcsd
  3. Oct 20, 2009 #2

    gabbagabbahey

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    Homework Helper
    Gold Member



    I assume you mean

    [tex]|\psi\rangle=A\begin{pmatrix}1-2i&2\end{pmatrix}^T=A\begin{pmatrix}1-2i\\2\end{pmatrix}[/tex]

    ???

    What is the matrix representation of [itex]S_x[/itex] in the z-basis? What are its eigenvalues and eigenvectors?
     
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