Principles of Quantum Mechanics · Problem 2.5.2

Review of Classical Mechanics — R. Shankar

Physics — Quantum Mechanics · hamiltonian-mechanics-phase-space-trajectories

Problem

Using the conservation of energy, show that the trajectories in phase space for the oscillator are ellipses of the form

(x/a)^2 + (p/b)^2 = 1

, where

a^2 = 2E/k

and

b^2 = 2mE