{"title":"球面三维谐振子的阶梯算子","authors":"João Marcos Costa Monteiro, E. Drigo Filho","doi":"10.1590/1806-9126-rbef-2020-0393","DOIUrl":null,"url":null,"abstract":"The Schrödinger equation for an isotropic three-dimensional harmonic oscillator is solved using ladder operators. The starting point is the shape invariance condition, obtained from supersymmetric quantum mechanics. Generalized ladder operators can be constructed for the three spherical spatial coordinates. Special emphasis is given to the adaptation made to each of these coordinates. The approach used is general and is indicated as an alternative method to solve the Schrödinger equation.","PeriodicalId":49620,"journal":{"name":"Revista Brasileira De Ensino De Fisica","volume":"51 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Ladder Operators for the Spherical 3D Harmonic Oscillator\",\"authors\":\"João Marcos Costa Monteiro, E. Drigo Filho\",\"doi\":\"10.1590/1806-9126-rbef-2020-0393\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The Schrödinger equation for an isotropic three-dimensional harmonic oscillator is solved using ladder operators. The starting point is the shape invariance condition, obtained from supersymmetric quantum mechanics. Generalized ladder operators can be constructed for the three spherical spatial coordinates. Special emphasis is given to the adaptation made to each of these coordinates. The approach used is general and is indicated as an alternative method to solve the Schrödinger equation.\",\"PeriodicalId\":49620,\"journal\":{\"name\":\"Revista Brasileira De Ensino De Fisica\",\"volume\":\"51 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Revista Brasileira De Ensino De Fisica\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1590/1806-9126-rbef-2020-0393\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Social Sciences\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Revista Brasileira De Ensino De Fisica","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1590/1806-9126-rbef-2020-0393","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Social Sciences","Score":null,"Total":0}
Ladder Operators for the Spherical 3D Harmonic Oscillator
The Schrödinger equation for an isotropic three-dimensional harmonic oscillator is solved using ladder operators. The starting point is the shape invariance condition, obtained from supersymmetric quantum mechanics. Generalized ladder operators can be constructed for the three spherical spatial coordinates. Special emphasis is given to the adaptation made to each of these coordinates. The approach used is general and is indicated as an alternative method to solve the Schrödinger equation.
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The Revista Brasileira de Ensino de Física - RBEF - is an open-access journal of the Brazilian Physical Society (SBF) devoted to the improvement of Physics teaching at all academic levels. Through the publication of peer-reviewed, high-quality papers, we aim at promoting Physics and correlated sciences, thus contributing to the scientific education of society. The RBEF accepts papers on theoretical and experimental aspects of Physics, materials and methodology, history and philosophy of sciences, education policies and themes relevant to the physics-teaching and research community.
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