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A) If two operators commute, show that they have the same eigenfunction. B) Prove that [A^, (B^ + C^)] = [A^, B^] + [A^, C^] C) Write the differential expression of the angular momentum components Lx, L, and L,. %3D

A) If two operators commute, show that they have the same eigenfunction. B) Prove that [A^, (B^ + C^)] = [A^, B^] + [A^, C^] C) Write the differential expression of the angular momentum components Lx, L, and L,. %3D

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A) If two operators commute, show that they have the same eigenfunction. B) Prove that [A^, (B^ + C^)] = [A^, B^] + [A^, C^] C) Write the differential expression of the angular momentum components Lx, L, and L,. D) Determine the value of the total angular momentum L for the H-atom in the orbit l=3 and plot a diagram to show its projections on the z-axis.
Transcribed Image Text:A) If two operators commute, show that they have the same eigenfunction. B) Prove that [A^, (B^ + C^)] = [A^, B^] + [A^, C^] C) Write the differential expression of the angular momentum components Lx, L, and L,. D) Determine the value of the total angular momentum L for the H-atom in the orbit l=3 and plot a diagram to show its projections on the z-axis.
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