Dear Sir, I am currently doing an advanced course in Quantum Mechanics. This current doubt of mine, I am unable to clarify it properly. It follows as: Spin 1/2 particles reside in 2dim-Hilbert space( Spinor Space)...However, we talk about rotations of states in this space where the angle of rotation is measured w.r.t Euclidean Space and we also build a Rotational Operator in this 2dim-space. My doubt is that why should spin states which reside in their own Hilbert Space respond to rotations that are carried in 3-dim Eucliean Space.? I was struck with this . Can you please help me to solve this ?