1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted