- #1

assyrian_77

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Let us say I have an [tex]S=1/2[/tex] dimer with [tex]H=JS_{1}\cdot S_{2}[/tex]. With a [tex]\hat{z}[/tex]-diagonal basis, [tex]|\uparrow\uparrow\rangle[/tex], [tex]|\uparrow\downarrow\rangle[/tex], [tex]|\downarrow\uparrow\rangle[/tex], [tex]|\downarrow\downarrow\rangle[/tex], I can easily construct the H-matrix by either using the Pauli matrices or the S-operators. Diagonalizing the matrix gives me the energy eigenvalues and the eigenvectors. Although I can get the energies in an easier way.

My problem/dilemma/question is this: What if I have an [tex]S=3/2[/tex] dimer (same form on H)? What [tex]\hat{z}[/tex]-diagonal basis (if any) can I use? And am I right in assuming that the matrices to use are the [tex]4\times4[/tex]-matrices listed in e.g. Schiff:

*Quantum Mechanics*(1968), page 203? (Don't feel like typing them right now)

And a bonus-question: Assuming now [tex]S=1[/tex]. What happens?

*I feel a bit silly for not knowing this*