English

Singular parametric oscillators from the one-parameter Darboux transformation of the classical harmonic oscillator

Classical Physics 2024-11-11 v2 Exactly Solvable and Integrable Systems

Abstract

The singular parametric oscillators obtained from the one-parameter Darboux deformation/transformation effected upon the classical harmonic oscillator are introduced and discussed in some detail using sin(omega_0 t) and cos(omega_0 t) as seed solutions. The corresponding Ermakov-Lewis integrability problem of these parametric oscillators is also studied. It is shown that the Ermakov-Lewis invariants do not depend on the deformation parameter and are singularity-free.

Keywords

Cite

@article{arxiv.2403.12084,
  title  = {Singular parametric oscillators from the one-parameter Darboux transformation of the classical harmonic oscillator},
  author = {H. C. Rosu and J. de la Cruz},
  journal= {arXiv preprint arXiv:2403.12084},
  year   = {2024}
}

Comments

16 pages, 10 figures, 35 references, published version, a few remaining misprints corrected