Exploring the Matrix Hamiltonian for Non-Identical Spin 1/2 Particles

[sevensixtwo]

Matrix Hamiltonian?

Homework Statement

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!

 

[theUndergrad]

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.


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theUndergrad

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