{"title":"Bargmann transform and statistical properties for nonlinear coherent states of the isotonic oscillator","authors":"Ghayth Ouirdani, Othmane El Moize","doi":"10.1515/zna-2023-0206","DOIUrl":null,"url":null,"abstract":"Abstract We construct a new class of nonlinear coherent states for the isotonic oscillator by replacing the factorial of the coefficients <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <m:msup> <m:mrow> <m:mi>z</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> </m:mrow> </m:msup> <m:mo>/</m:mo> <m:msqrt> <m:mrow> <m:mi>n</m:mi> <m:mo>!</m:mo> </m:mrow> </m:msqrt> </m:math> ${z}^{n}/\\sqrt{n!}$ of the canonical coherent states by the factorial <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <m:msubsup> <m:mrow> <m:mi>x</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> </m:mrow> <m:mrow> <m:mi>γ</m:mi> </m:mrow> </m:msubsup> <m:mo>!</m:mo> <m:mo>=</m:mo> <m:msubsup> <m:mrow> <m:mi>x</m:mi> </m:mrow> <m:mrow> <m:mn>1</m:mn> </m:mrow> <m:mrow> <m:mi>γ</m:mi> </m:mrow> </m:msubsup> <m:mo>.</m:mo> <m:msubsup> <m:mrow> <m:mi>x</m:mi> </m:mrow> <m:mrow> <m:mn>2</m:mn> </m:mrow> <m:mrow> <m:mi>γ</m:mi> </m:mrow> </m:msubsup> <m:mo>…</m:mo> <m:msubsup> <m:mrow> <m:mi>x</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> </m:mrow> <m:mrow> <m:mi>γ</m:mi> </m:mrow> </m:msubsup> </m:math> ${x}_{n}^{\\gamma }!={x}_{1}^{\\gamma }.{x}_{2}^{\\gamma }\\dots {x}_{n}^{\\gamma }$ with <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <m:msubsup> <m:mrow> <m:mi>x</m:mi> </m:mrow> <m:mrow> <m:mn>0</m:mn> </m:mrow> <m:mrow> <m:mi>γ</m:mi> </m:mrow> </m:msubsup> <m:mo>=</m:mo> <m:mn>0</m:mn> </m:math> ${x}_{0}^{\\gamma }=0$ , where <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <m:msubsup> <m:mrow> <m:mi>x</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> </m:mrow> <m:mrow> <m:mi>γ</m:mi> </m:mrow> </m:msubsup> </m:math> ${x}_{n}^{\\gamma }$ is a sequence of positive numbers and γ is a positive real parameter. This also leads to the construction of a Bargmann-type integral transform which will allow us to find some integral transforms for orthogonal polynomials. The statistics of our coherent states will also be considered by the calculus of one called Mandel parameter. The squeezing phenomenon was also discussed.","PeriodicalId":54395,"journal":{"name":"Zeitschrift Fur Naturforschung Section A-A Journal of Physical Sciences","volume":"25 11","pages":"0"},"PeriodicalIF":1.8000,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Zeitschrift Fur Naturforschung Section A-A Journal of Physical Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/zna-2023-0206","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"CHEMISTRY, PHYSICAL","Score":null,"Total":0}
引用次数: 0
Abstract
Abstract We construct a new class of nonlinear coherent states for the isotonic oscillator by replacing the factorial of the coefficients zn/n! ${z}^{n}/\sqrt{n!}$ of the canonical coherent states by the factorial xnγ!=x1γ.x2γ…xnγ ${x}_{n}^{\gamma }!={x}_{1}^{\gamma }.{x}_{2}^{\gamma }\dots {x}_{n}^{\gamma }$ with x0γ=0 ${x}_{0}^{\gamma }=0$ , where xnγ ${x}_{n}^{\gamma }$ is a sequence of positive numbers and γ is a positive real parameter. This also leads to the construction of a Bargmann-type integral transform which will allow us to find some integral transforms for orthogonal polynomials. The statistics of our coherent states will also be considered by the calculus of one called Mandel parameter. The squeezing phenomenon was also discussed.
期刊介绍:
A Journal of Physical Sciences: Zeitschrift für Naturforschung A (ZNA) is an international scientific journal which publishes original research papers from all areas of experimental and theoretical physics. Authors are encouraged to pay particular attention to a clear exposition of their respective subject, addressing a wide readership. In accordance with the name of our journal, which means “Journal for Natural Sciences”, manuscripts submitted to ZNA should have a tangible connection to actual physical phenomena. In particular, we welcome experiment-oriented contributions.