Quantum Mechanics (1) · Problem 5.3

Rotations and angular momentum

Physics — Quantum Mechanics · su2-uniqueness-multiple-of-identity

Problem

Suppose

u_1 \in SU(2)

and

u_2 \in SU(2)

are such that

u_1 X u_1^\dagger = u_2 X u_2^\dagger, \quad \forall X \in V_3. \tag{5.67}

Show that

u_2^{-1} u_1

commutes with every

X \in V_3

and therefore this matrix must be a multiple of the identity.