Using the two spin functions phi1 alpha and alpha2 beta as

Using the two spin functions phi_1 = alpha and alpha_2 = beta as an orthonormal basis (so (alpha| alpha) = (beta|beta) = 0), and the relations S_x alpha = 1/2 beta, S_x beta = 1/2 alpha, S_y alpha = 1/2 i beta, S_y beta = -1/2 I alpha, S_z alpha = 1/2 alpha = 1/2 alpha, S_z beta = -1/2 beta, construct the 2 time 2 matrices of S_x, S_y, and S_z. Taking now the basis phi\'_1 = C(alpha + beta), phi\'_2 = C(alpha - beta): Verify that phi\'_1 and phi\'_2 are orthogonal, Assign C a value that makes phi\'_1 and phi_2\' normalized, Find the unitary matrix for the transformation [phi_i} rightarrow {phi\'_i} Find the matrices of S_x, S_y, and S_z in the {phi\'_i} basis.

Solution

Ans-

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