Vol 3 - Landau, Lifshitz - Quantum mechanics - non-relativistic theory (3ed., 1991) · Problem P2

Motion in a Centrally Symmetric Field

Physics — Landau & Lifshitz · tensor-average-angular-momentum

Problem

Average the tensor

n_in_k - \frac{1}{3}\delta_{ik}

(where

\mathbf{n}

is a unit vector along the radius vector of a particle) over a state where the magnitude but not the direction of the vector

\mathbf{l}

is given (i.e.\

l_z

is indeterminate).