Question

5. (4 pts) Prove that $[\hat{L}^2, \hat{L}_z] = 0$ using the following identities: (a) $\hat{L}^2 = \hat{L}_x^2 + \hat{L}_y^2 + \hat{L}_z^2$ (b) $[A + B + C, D] = [A, D] + [B, D] + [C, D]$ (c) $[AB, C] = A[B, C] + [A, C]B$

          5. (4 pts) Prove that $[\hat{L}^2, \hat{L}_z] = 0$ using the following identities:
(a) $\hat{L}^2 = \hat{L}_x^2 + \hat{L}_y^2 + \hat{L}_z^2$
(b) $[A + B + C, D] = [A, D] + [B, D] + [C, D]$
(c) $[AB, C] = A[B, C] + [A, C]B$

5. (4 pts) Prove that [L̂^2, L̂z] = 0 using the following identities:
(a) L̂^2 = L̂x^2 + L̂y^2 + L̂z^2
(b) [A + B + C, D] = [A, D] + [B, D] + [C, D]
(c) [AB, C] = A[B, C] + [A, C]B

Added by Claire B.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Deepak Jangra

Step 1

First, let's use the identity [A+B+C,D]=[A,D]+[B,D]+[C,D] to expand [L^2,L]: [L^2,L] = [L,L]+[L,L] = 2[L,L] Show more…

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Prove that [L^2,L]=0 using the following identities: [A+B+C,D]=[A,D]+[B,D]+[C,D], [AB,C]=A[B,C]+[A,C]B.

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Question

5. (4 pts) Prove that $[\hat{L}^2, \hat{L}_z] = 0$ using the following identities: (a) $\hat{L}^2 = \hat{L}_x^2 + \hat{L}_y^2 + \hat{L}_z^2$ (b) $[A + B + C, D] = [A, D] + [B, D] + [C, D]$ (c) $[AB, C] = A[B, C] + [A, C]B$

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