Operators Lz, Lx, and Ly are given in matrix form as: Lz = a5 Lx = La Ly = L Using the above matrices, show that the following commutation relations hold: [Lx, Ly] = iLz [Lx, Lz] = iLy
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Step 1: Calculate the matrix multiplication for [L̂+, L̂z] = L̂+L̂z - L̂zL̂+ First calculate L̂+L̂z: L̂+L̂z = [0 √2 0; 0 0 √2; 0 0 0] × [1 0 0; 0 0 0; 0 0 -1] = [0×1 + √2×0 + 0×0, 0×0 + √2×0 + 0×0, 0×0 + √2×0 + 0×(-1); 0×1 + 0×0 + √2×0, 0×0 + 0×0 + Show more…
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