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Homework Help: Spin eigenfunctions for two particles

  1. Jul 7, 2008 #1
    1. The problem statement, all variables and given/known data
    Consider two identical particles of mass [tex]m[/tex] and spin 1/2. They interact via a potential given by

    [tex] V = \frac{g}{r} \sigma_{1} \sigma{2}[/tex]

    where [tex]g>0[/tex] and [tex] \sigma_{j} [/tex] are Pauli spin matrices which operate on the spin of particle j.

    (a) Construct the spin eigenfunctions for the two particle states. What is the expectation value of V for each of these states?

    (b) Give eigenvalues of all the bounded states.

    2. Relevant equations

    [tex] \sigma_{1} = \left( \stackrel{0}{1} \stackrel{1}{0}\right)[/tex]
    [tex] \sigma_{2} = \left( \stackrel{0}{i} \stackrel{-i}{0}\right)[/tex]
    [tex] \sigma_{3} = \left( \stackrel{1}{0} \stackrel{0}{-1}\right)[/tex]

    3. The attempt at a solution

    Other than finding the Pauli Spin matrices, I don't know how to go about solving this problem. I have Griffiths QM text, so feel free to refer to that when giving pointers as how to proceed. Thanks.
  2. jcsd
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