为一类扩展的截断卡洛吉罗-萨瑟兰模型生成支持零能量可归一化状态的 QES 势

IF 3 3区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY
Satish Yadav , Sudhanshu Shekhar , Bijan Bagchi , Bhabani Prasad Mandal
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引用次数: 0

摘要

最近,人们热衷于寻找底层薛定谔方程可解的势,受此激励,我们在最近的工作中报告了几种情况,即零能态根据定义势的耦合常数的某些限制而变得受约束。在这方面,我们提出了证据,证明准精确可解(QES)势系统存在有规则的零能可归一化解,该系统对应于合理扩展的多体截断卡洛吉罗-萨瑟兰(TCS)模型。我们的程序基于使用标准势组方法,其基本结构为 so(2,1),利用点规范变换,出现了三种具有相同特征值的不同类型势,而它们的共同特性则受制于相关波函数的评估。通过适当限制耦合参数,可以单独处理这些情况。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Generating QES potentials supporting zero energy normalizable states for an extended class of truncated Calogero Sutherland model
Motivated by recent interest in the search for generating potentials for which the underlying Schrödinger equation is solvable, we report in the recent work several situations when a zero-energy state becomes bound depending on certain restrictions on the coupling constants that define the potential. In this regard, we present evidence of the existence of regular zero-energy normalizable solutions for a system of quasi-exactly solvable (QES) potentials that correspond to the rationally extended many-body truncated Calogero–Sutherland (TCS) model. Our procedure is based upon the use of the standard potential group approach with an underlying so(2,1) structure that utilizes a point canonical transformation with three distinct types of potentials emerging having the same eigenvalues while their common properties are subjected to the evaluation of the relevant wave functions. These cases are treated individually by suitably restricting the coupling parameters.
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来源期刊
Annals of Physics
Annals of Physics 物理-物理:综合
CiteScore
5.30
自引率
3.30%
发文量
211
审稿时长
47 days
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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