{"title":"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","authors":"Satish Yadav , Sudhanshu Shekhar , Bijan Bagchi , Bhabani Prasad Mandal","doi":"10.1016/j.aop.2024.169822","DOIUrl":null,"url":null,"abstract":"<div><div>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 <span><math><mrow><mi>s</mi><mi>o</mi><mrow><mo>(</mo><mn>2</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span> 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.</div></div>","PeriodicalId":8249,"journal":{"name":"Annals of Physics","volume":"470 ","pages":"Article 169822"},"PeriodicalIF":3.0000,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Generating QES potentials supporting zero energy normalizable states for an extended class of truncated Calogero Sutherland model\",\"authors\":\"Satish Yadav , Sudhanshu Shekhar , Bijan Bagchi , Bhabani Prasad Mandal\",\"doi\":\"10.1016/j.aop.2024.169822\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>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 <span><math><mrow><mi>s</mi><mi>o</mi><mrow><mo>(</mo><mn>2</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span> 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.</div></div>\",\"PeriodicalId\":8249,\"journal\":{\"name\":\"Annals of Physics\",\"volume\":\"470 \",\"pages\":\"Article 169822\"},\"PeriodicalIF\":3.0000,\"publicationDate\":\"2024-10-15\",\"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/S000349162400229X\",\"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}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Physics","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S000349162400229X","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}
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 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.
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.
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