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Identical Particles — Nouredine Zettili
Physics — Quantum Mechanics · spherical-tensors-commutation-relations
Problem Prove the following commutation relations:
(a) [ J x , [ J x , T q ( k ) ] ] = ∑ q ′ T q ′ ( k ) ⟨ k , q ′ ∣ J x 2 ∣ k , q ⟩ \left[J_x,\,[J_x,\,T^{(k)}_q]\right] = \sum_{q'} T^{(k)}_{q'}\langle k,\,q'\mid J_x^2\mid k,\,q\rangle [ J x , [ J x , T q ( k ) ] ] = ∑ q ′ T q ′ ( k ) ⟨ k , q ′ ∣ J x 2 ∣ k , q ⟩ [ J x , [ J x , T q ( k ) ] ] + [ J y , [ J y , T q ( k ) ] ] + [ J z , [ J z , T q ( k ) ] ] = k ( k + 1 ) ℏ 2 T q ( k ) \left[J_x,\,[J_x,\,T^{(k)}_q]\right] + \left[J_y,\,[J_y,\,T^{(k)}_q]\right] + \left[J_z,\,[J_z,\,T^{(k)}_q]\right] = k(k+1)\hbar^2 T^{(k)}_q [ J x , [ J x , T q ( k ) ] ] + [ J y , [ J y , T q ( k ) ] ] + [ J z , [ J z , T q ( k ) ] ] = k ( k + 1 ) ℏ 2 T q ( k ) Browse the problem library