Question

The antisymmetric exchange interaction of two electron spins σ1 and σ2 is given by Hamiltonian operator H = A · (σ1 × σ2),Furthermore, the direct product of two single spin subspaces is meant, so that the resulting Hilbert space of spins is a 4x4 matrix. Is the square of the total spin of two electrons conserved?

Answer 1

Yes the square of the total spin of two electrons is conserved ( s^2)

Explanation:

using the Hamiltonian operator H = A · (σ1 × σ2)

S = ( S1 + S2 )

S^2 = S²₁ + S²₂ + 2S₂ . S₂ ( apply the equation of time evolution )

Attached below is the detailed solution