SU(2) Adjoint Orbit

Generator axis: Rotation speed ω: 1.0 Second axis (free): 0.0 Initial state θ: 45° N particles: 50

su(2) generators:

Jₓ,Jᵧ,J_z basis

[Jₓ,Jᵧ] = iJ_z

Adj orbit of p ∈ su(2):

sphere S² of fixed |p|

State on Bloch sphere:

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SU(2) adjoint action: Ad_g(X) = gXg⁻¹. Orbits in su(2) ≅ ℝ³ are 2-spheres of fixed radius. Commutator flow [H,X] = adₕ(X) generates rotations on Bloch sphere. Spin-1/2 dynamics.