Vol 1 - L D Landau, E.M. Lifshitz - Mechanics · Problem 42.4

The Canonical Equations

Physics — Landau & Lifshitz · poisson-brackets

Problem

Show that

[\mathbf{f}, M_z] = \mathbf{f} \times \mathbf{n}

, where

\mathbf{f}

is a vector function of the co-ordinates and momentum of a particle, and

\mathbf{n}

is a unit vector parallel to the

z

-axis.