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Homework Help: Find matrix for total angular momentum along y; find eigenvalues and eigenvectors.

  1. Apr 14, 2012 #1
    1. The problem statement, all variables and given/known data

    Consider the angular momentum operator [itex]\vec{J_{y}}[/itex] in the subspace for which j=1. Write down the matrix for this operator in the usual basis (where [itex]J^{2}[/itex] and [itex]J_{z}[/itex] are diagonal). Diagonalize the matrix and find the eigenvalues and orthonormal eigenvectors.

    2. Relevant equations

    [itex]\vec{J} = \vec{L} + \vec{S}[/itex] (total angular momentum)

    3. The attempt at a solution

    I know J is the sum of angular momentum, L, and spin angular momentum, S, but how to we get it in matrix form? Spin would just be [itex]\hbar / 2[/itex] times the y Pauli matrix... but how do we express L in matrix form? Also, I really don't understand how to obtain eigenvalues and eigenvectors... Could someone go through the problem for me? Textbook is Griffiths. Thanks in advance.
  2. jcsd
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