Demystifying the constancy of the Ermakov-Lewis invariant for a time dependent oscillator

Abstract

It is well known that the time dependent harmonic oscillator possesses a conserved quantity, usually called Ermakov-Lewis invariant. I provide a simple physical interpretation of this invariant as well as a whole family of related invariants. This interpretation does not seem to have been noticed in the literature before. The procedure also allows one to tackle some key conceptual issues which arise in the study of quantum fields in external, time dependent, backgrounds like in the case of particle production in an expanding universe and Schwinger effect.

5 pages; no figures

Cited by in corpus (13)

• Cosmological aspects of the Eisenhart-Duval lift
• Quantum-gravity effects for excited states of inflationary perturbations
• Inverting a normal harmonic oscillator: Physical interpretation and applications
• Coherent states for exactly solvable time-dependent oscillators generated by Darboux transformations
• Quantum nonstationary oscillators: Invariants, dynamical algebras and coherent states via point transformations
• No-boundary Wave Function, Wheeler-DeWitt Equation and Path Integral Analysis of the Bouncing `Quantum' Cosmology
• Generalized Schwinger effect and particle production in an expanding universe
• Comment on Demystifying the constancy of the Ermakov-Lewis invariant for a time-dependent oscillator
• Symmetries and conservation laws for the generalized $n$-dimensional Ermakov system
• Dirac-isotonic oscillators in (1 + 1) and (2 + 1) dimensions
• Complex time route to quantum backreaction
• Quantum Uncertainty as an Intrinsic Clock
• Nonlocal transformations of the Generalized Liénard type equations and dissipative Ermakov-Milne-Pinney systems