Principles of Quantum Mechanics · Problem 2.7.2

Review of Classical Mechanics — R. Shankar

Physics — Quantum Mechanics · poisson-brackets-canonical-equations

Problem

(i) Verify Eqs. (2.7.4) and (2.7.5). (ii) Consider a problem in two dimensions given by

\mathscr{H} = p_x^2 + p_y^2 + ax^2 + by^2

. Argue that if

a = b

\{l_z, \mathscr{H}\}

must vanish. Verify by explicit computation.