# Homework Help: Matrix Hamiltonian?

1. Jun 27, 2008

### sevensixtwo

Matrix Hamiltonian???

1. The problem statement, all variables and given/known data

I have two non-identical spin 1/2 particles, which have vector magnetic moments S_1 and S_2. The interaction energy (Hamiltonian) is given by a constant times the dot product of S_1 and S_2. There is no external field present.

I need to find the eigenstates and eigenenergies, which I could easily do if the Hamiltonian was given as a matrix. Is there a way to write this H as a matrix or is there perhaps another way to find the eigen-items?

Thanks so much for any input!!

2. Jun 27, 2008

Since these spin-1/2 particles there are only two possible eigenstates for each of the particles: either S=(1,0)$$^{T}$$ or (0,1)$$^{T}$$. Since these are non interacting particles, either one can be in either state, so you have 4 possible configurations for the system. Then it's just a matter of chugging through the algebra.