Quantum Mechanics: Concepts and Applications · Problem 7.18

Identical Particles — Nouredine Zettili

Physics — Quantum Mechanics · wigner-eckart-theorem-spherical-tensors

Problem

(a) Express

xz/r^2

and

(x^2 - y^2)/r^2

in terms of the components of a spherical tensor of rank 2. (b) Using the Wigner–Eckart theorem, calculate the values of

\langle 1,\,0\mid xz/r^2\mid 1,\,1\rangle

and

\langle 1,\,1\mid (x^2-y^2)/r^2\mid 1,\,-1\rangle