KvN mechanics approach to the time-dependent frequency harmonic oscillator.

Abstract:

:Using the Ermakov-Lewis invariants appearing in KvN mechanics, the time-dependent frequency harmonic oscillator is studied. The analysis builds upon the operational dynamical model, from which it is possible to infer quantum or classical dynamics; thus, the mathematical structure governing the evolution will be the same in both cases. The Liouville operator associated with the time-dependent frequency harmonic oscillator can be transformed using an Ermakov-Lewis invariant, which is also time dependent and commutes with itself at any time. Finally, because the solution of the Ermakov equation is involved in the evolution of the classical state vector, we explore some analytical and numerical solutions.

journal_name

Sci Rep

journal_title

Scientific reports

authors

Ramos-Prieto I,Urzúa-Pineda AR,Soto-Eguibar F,Moya-Cessa HM

doi

10.1038/s41598-018-26759-w

subject

Has Abstract

pub_date

2018-05-30 00:00:00

pages

8401

issue

1

issn

2045-2322

pii

10.1038/s41598-018-26759-w

journal_volume

8

pub_type

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