Spin eigenfunctions for two particles

1. Jul 7, 2008

SonOfOle

1. The problem statement, all variables and given/known data
Consider two identical particles of mass $$m$$ and spin 1/2. They interact via a potential given by

$$V = \frac{g}{r} \sigma_{1} \sigma{2}$$

where $$g>0$$ and $$\sigma_{j}$$ 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

$$\sigma_{1} = \left( \stackrel{0}{1} \stackrel{1}{0}\right)$$
$$\sigma_{2} = \left( \stackrel{0}{i} \stackrel{-i}{0}\right)$$
$$\sigma_{3} = \left( \stackrel{1}{0} \stackrel{0}{-1}\right)$$

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.