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

H. C. Rosu; J. de la Cruz

doi:10.1016/j.aop.2024.169830

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arXiv · 2403.12084

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

H. C. Rosu·J. de la Cruz

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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.

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H. C. Rosu, J. de la Cruz. 2024-03-07. Singular parametric oscillators from the one-parameter Darboux transformation of the classical harmonic oscillator. https://doi.org/10.1016/j.aop.2024.169830

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