{"title":"The Particle in a Box Warrants an Examination","authors":"J. Klauder","doi":"10.4236/jhepgc.2022.83043","DOIUrl":null,"url":null,"abstract":"The particle in a box is a simple model that has a classical Hamiltonian H = p 2 (using 2 m = 1), with a limited coordinate space, − b < q < b , where 0 < b < ∞ . Using canonical quantization, this example has been fully studied thanks to its simplicity, and it is a common example for beginners to understand. Despite its repeated analysis, there is a feature that puts the past results into question. In addition to pointing out the quantization issue, the procedures of affine quantization can lead to a proper quantization that nesaeccsrily points toward more complicated eigenfunctions and eigenvalues, which deserve to be solved.","PeriodicalId":59175,"journal":{"name":"高能物理(英文)","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2022-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"高能物理(英文)","FirstCategoryId":"1089","ListUrlMain":"https://doi.org/10.4236/jhepgc.2022.83043","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
Abstract
The particle in a box is a simple model that has a classical Hamiltonian H = p 2 (using 2 m = 1), with a limited coordinate space, − b < q < b , where 0 < b < ∞ . Using canonical quantization, this example has been fully studied thanks to its simplicity, and it is a common example for beginners to understand. Despite its repeated analysis, there is a feature that puts the past results into question. In addition to pointing out the quantization issue, the procedures of affine quantization can lead to a proper quantization that nesaeccsrily points toward more complicated eigenfunctions and eigenvalues, which deserve to be solved.