a Prove that (1 2) (1 ix) acting on a two component spinor can be regarded as the matrix representation of the rotation operator about the x axis by angle 2 (The minus sign signifies that the rotation is clockwise ) b Construct the matrix representation of Sz when the eigenkets of Sy are used as base vectors

Question: a. Prove that (1/2) (1 + ix) acting on a two-component spinor can be regarded as the matrix representation of the rotation operator about the

a. Prove that (1/√2) (1 + iσx) acting on a two-component spinor can be regarded as the matrix representation of the rotation operator about the x-axis by angle – π/2. (The minus sign signifies that the rotation is clockwise.)

b. Construct the matrix representation of Sz when the eigenkets of Sy are used as base vectors.

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