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Using the rotation operator to solve for eigenstates upon a general basis

  1. Nov 10, 2012 #1
    1. The problem statement, all variables and given/known data

    I need to express the rotation operator as follows

    R(uj) = cos(u/2) + 2i(\hbar) S_y sin(u/2)

    given the fact that

    R(uj)= e^(iuS_y/(\hbar))

    using |+-z> as a basis,
    expanding R in a taylor series
    express S_y^2 as a matrix

    2. Relevant equations

    I know
    e^(ix)=cos(x)+isin(x)

    using this alone I can show this equivalence



    3. The attempt at a solution


    e^(ix)=cos(x)+isin(x)

    which implies

    R(uj)= e^(iuS_y/(\hbar)) = cos(uS_y/(\hbar)+isin(uS_y/(\hbar)

    S_y = (\hbar)/2

    Therefore

    R(uj)= e^(iuS_y/(\hbar)) = cos(u/2)+iS_y*sin(u/2)



    ... What's this about finding the matrix representation of S_y^2 ?
     
  2. jcsd
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