Two helpful developments towards better understanding of adiabatic invariance in classical mechanics

Abstract

Abstract The topic of difficult understanding of adiabatic invariance in classical mechanics is dealt with in a more understandable way. Using the one-dimensional harmonic oscillator as an example, the goals of this paper are twofold. First, given a first-order parameter variation, the second-order magnitude of the correction to the adiabatic invariant is established in simple terms. Second, the identification of the action variable with the invariant quantity for slow variations of different parameters of the Hamiltonian is confirmed, by invoking the correct equation of motion in the derivation.

Keywords

• Adiabatic invariant
• classical mechanics