PHYSICS · Subjective · Fermi University Physics · Quantum Mechanics · Symmetry, angular momentum and spin · Symmetry, angular momentum and spin
The Structure of Quantum Mechanics, Ch Adding angular momenta, tensor operators and Wigner-Eckart
Problem
An atom is in a level with j=1. The spherical components of its magnetic dipole moment form a rank-1 tensor operator T^q(1) acting within this multiplet, with reduced matrix element ⟨1∥T^(1)∥1⟩=−3.2μB, where μB is the Bohr magneton.The Clebsch-Gordan coefficient for coupling j=1 to k=1 back to J=1 includes ⟨j=1,m=−1;k=1,q=1∣J=1,M=0⟩=−1/2, obtained from the ladder construction for 1⊗1. Use the Wigner-Eckart theorem, ⟨j′,m′∣T^q∣j,m⟩=⟨j,m;k,q∣j′,m′⟩⟨j′∥T^∥j⟩/2j′+1, to find ⟨1,0∣T^1(1)∣1,−1⟩.