Indian Journal of Physics

, Volume 91, Issue 4, pp 371–376 | Cite as

Use of quantum self-friction potentials and forces in standard convention for study of harmonic oscillator

  • I. I. Guseinov
  • B. A. Mamedov
Original Paper


In this paper, the physical nature of quantum usual and self-friction (SF) harmonic oscillators is presented. The procedure for studying these harmonic oscillators is identical; therefore, we can benefit from the theory of the usual harmonic oscillator. To study the SF harmonic oscillator, using analytical formulae for the \(L^{{(p_{l}^{ * } )}}\)-SF Laguerre polynomials (\(L^{{(p_{l}^{ * } )}}\)-SFLPs) and \(L^{{(\alpha^{*} )}}\)-modified SFLPs (\(L^{{(\alpha^{*} )}}\)-MSFLPs) in standard convention, the \(V^{{(p_{l}^{ * } )}}\)-SF potentials (\(V^{{(p_{l}^{ * } )}}\)-SFPs), \(V^{{(\alpha^{*} )}}\)-modified SFPs (\(V^{{(\alpha^{*} )}}\)-MSFPs), \(F^{{(p_{l}^{ * } )}}\)-SF forces (\(F^{{(p_{l}^{ * } )}}\)-SFFs) and \(F^{{(\alpha^{*} )}}\)-modified SFFs (\(F^{{(\alpha^{*} )}}\)-MSFFs) are investigated, where \(p_{l}^{ * } = 2l + 2 - \alpha^{*}\) and \(\,\alpha^{*}\) is the integer (\(\alpha^{*} = \alpha\), \(\, - \infty < \alpha \le 2)\) or non-integer (\(\alpha^{*} \ne \alpha\), \(\, - \infty < \alpha < 3)\) SF quantum number. We note that the potentials (\(V^{{(p_{l}^{ * } )}}\)-SFPs and \(V^{{(\alpha^{*} )}}\)-MSFPs), and forces (\(F^{{(p_{l}^{ * } )}}\)-SFFs and \(F^{{(\alpha^{*} )}}\)-MSFFs), respectively, are independent functions. It is shown that the numerical values of these independent functions are the same, i.e., \(V_{num}^{{(p_{l}^{ * } )}} = V_{num}^{{(\alpha^{*} )}}\) and \(F_{num}^{{(p_{l}^{ * } )}} = F_{num}^{{(\alpha^{*} )}}\). The dependence of the SF harmonic oscillator as a function of the distance is analyzed. The presented relationships are valid for arbitrary values of parameters.


Harmonic oscillator Standard convention Laguerre polynomials Self-friction quantum numbers 

PACS Numbers

31.10.+z 31.15.a- 


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Copyright information

© Indian Association for the Cultivation of Science 2016

Authors and Affiliations

  1. 1.Department of Physics, Faculty of Arts and SciencesOnsekiz Mart UniversityÇanakkaleTurkey
  2. 2.Department of Physics, Faculty of Arts and SciencesGaziosmanpaşa UniversityTokatTurkey
  3. 3.Department of PhysicsBaku State UniversityBakuAzerbaijan

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