A spin-3/2 particle (labeled 1) and a spin-1/2 particle (labeled 2) are interacting via(adsbygoogle = window.adsbygoogle || []).push({});

the Hamiltonian

[tex] \lambda \vec S_1 \cdot \vec S_2 + g(S_{1z} + S_{2z})^2[/tex]

where S1 is the spin operator of particle 1 (the spin-3/2) and S2 is the spin operator

of particle 2 (the spin-1/2). λ and g are positive constants (λ ≫ g).

I am asked to find the eigenstates and the corresponding energies for this hamiltonian (neglecting any spatial degrees of freedom).

Since we have a two particle system I guess one must consider addition of angular momenta and the CB-coefficients, but I am really unsure about this hamiltonian. Should one reformulate in in terms of total spin operators? Do we know how the total spin operator S acts without squaring it?

How do I get started here?

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# Eigenstates of composite spin hamiltoninan

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