Singular parametric oscillators from the one-parameter Darboux transformation of the classical harmonic oscillator
arXiv:2403.12084 · doi:10.1016/j.aop.2024.169830
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.
16 pages, 10 figures, 35 references, published version, a few remaining misprints corrected