Principles of Quantum Mechanics · Problem 2.7.1

Review of Classical Mechanics — R. Shankar

Physics — Quantum Mechanics · poisson-brackets-properties

Problem

Show that

\begin{aligned} \{\omega, \lambda\} &= -\{\lambda, \omega\} \\ \{\omega, \lambda + \sigma\} &= \{\omega, \lambda\} + \{\omega, \sigma\} \\ \{\omega, \lambda\sigma\} &= \{\omega, \lambda\}\sigma + \lambda\{\omega, \sigma\} \end{aligned}

Note the similarity between the above and Eqs. (1.5.10) and (1.5.11) for commutators.