{"title":"Singular parametric oscillators from the one-parameter Darboux transformation of the classical harmonic oscillator","authors":"","doi":"10.1016/j.aop.2024.169830","DOIUrl":null,"url":null,"abstract":"<div><div>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 <span><math><mrow><mo>sin</mo><mrow><mo>(</mo><msub><mrow><mi>ω</mi></mrow><mrow><mn>0</mn></mrow></msub><mi>t</mi><mo>)</mo></mrow></mrow></math></span> and <span><math><mrow><mo>cos</mo><mrow><mo>(</mo><msub><mrow><mi>ω</mi></mrow><mrow><mn>0</mn></mrow></msub><mi>t</mi><mo>)</mo></mrow></mrow></math></span> as seed solutions. The corresponding Ermakov–Lewis integrability problem of these parametric oscillators is also studied. It is shown that their Ermakov–Lewis invariants do not depend on the deformation parameter and are singularity-free.</div></div>","PeriodicalId":8249,"journal":{"name":"Annals of Physics","volume":null,"pages":null},"PeriodicalIF":3.0000,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Physics","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0003491624002379","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
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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 and as seed solutions. The corresponding Ermakov–Lewis integrability problem of these parametric oscillators is also studied. It is shown that their Ermakov–Lewis invariants do not depend on the deformation parameter and are singularity-free.
期刊介绍：
Annals of Physics presents original work in all areas of basic theoretic physics research. Ideas are developed and fully explored, and thorough treatment is given to first principles and ultimate applications. Annals of Physics emphasizes clarity and intelligibility in the articles it publishes, thus making them as accessible as possible. Readers familiar with recent developments in the field are provided with sufficient detail and background to follow the arguments and understand their significance.
The Editors of the journal cover all fields of theoretical physics. Articles published in the journal are typically longer than 20 pages.
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