Review of Braket notation
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Moving toward the interaction of two spins

(pic) Set up one spin Braket notation

(pic) some spin geometry, showing how certain currents attract eachother


                            Two Spins
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Chapter 5 - Two Spins

(pic) 𝐒₁⋅𝐒₂  OR 2A/ħ²𝐒₁⋅𝐒₂ in book

hydrogen spin-orbit hamiltonian Ĥ = -γ 𝐒⋅𝐋

4 possible states

    ❙S₁𝓏=+½ S₂𝓏=+½❭ = ❙½❭⨂❙½❭
    ❙S₁𝓏=+½ S₂𝓏=-½❭
    ❙S₁𝓏=-½ S₂𝓏=+½❭
    ❙S₁𝓏=-½ S₂𝓏=-½❭

        (pic) expanded ❙½❭⨂❙½❭


(pic x2) finding representations for all of the operators in the two-spin system

(pic) Worked out some operations on various possible states, using direct product spaces

(pic x2) Diagonalized 𝐒₁⋅𝐒₂

    !!! missing a factor of 2 somewhere in these pictures