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Spin
Physics — Quantum Mechanics · commutation-conservation-laws
Problem Show [ H , L ] = 0 [H, \boldsymbol{L}] = 0 [ H , L ] = 0 [ H , P ] = 0 [H, \boldsymbol{P}] = 0 [ H , P ] = 0 H = ∑ n = 1 N p n 2 2 m n + 1 2 ∑ n , n ′ V ( ∣ x n − x n ′ ∣ ) , L = ∑ n = 1 N x n × p n , P = ∑ n = 1 N p n , H = \sum_{n=1}^{N} \frac{\boldsymbol{p}_n^2}{2m_n} + \frac{1}{2}\sum_{n,n'} V(|\boldsymbol{x}_n - \boldsymbol{x}_{n'}|), \quad \boldsymbol{L} = \sum_{n=1}^{N} \boldsymbol{x}_n \times \boldsymbol{p}_n, \quad \boldsymbol{P} = \sum_{n=1}^{N} \boldsymbol{p}_n, H = n = 1 ∑ N 2 m n p n 2 + 2 1 n , n ′ ∑ V ( ∣ x n − x n ′ ∣ ) , L = n = 1 ∑ N x n × p n , P = n = 1 ∑ N p n , L \boldsymbol{L} L P \boldsymbol{P} P Browse the problem library