{"title":"确定自旋为 0 的粒子的费什巴赫-维拉斯振荡器的香农熵和费雪信息","authors":"A. Boumali, A. Hamla, Y. Chargui","doi":"10.1007/s10773-024-05743-3","DOIUrl":null,"url":null,"abstract":"<p>This paper is devoted to calculating the Fisher and Shannon information parameters of the Feshbach-Villars oscillator (FVO) for spin-0 particles. Instead of the Klein-Gordon equation, the Feshbach-Villars formalism provides a positive probability density. By determining Fisher information and Shannon entropy, we assess the sensitivity of probability distributions to parameter changes and the degree of uncertainty. Our research provides insights into the dynamics and information-theoretic characteristics of spin-0 particles in both spatial and momentum configurations. This work advances our understanding of the quantum information properties of spin-0 particles and lays the groundwork for future developments in quantum computing and information theory. Finally, the Stam, Cramer–Rao, and Bialynicki–Birula–Mycielski (BBM) inequalities have been verified, and we demonstrated that the BBM inequality remains valid in the form <span>\\(S_{x}+S_{p}\\ge 1+\\ln \\pi \\)</span>, consistent with ordinary quantum mechanics.</p>","PeriodicalId":597,"journal":{"name":"International Journal of Theoretical Physics","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2024-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Determination of Shannon entropy and Fisher information of the Feshbach-Villars oscillator for spin-0 particles\",\"authors\":\"A. Boumali, A. Hamla, Y. Chargui\",\"doi\":\"10.1007/s10773-024-05743-3\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>This paper is devoted to calculating the Fisher and Shannon information parameters of the Feshbach-Villars oscillator (FVO) for spin-0 particles. Instead of the Klein-Gordon equation, the Feshbach-Villars formalism provides a positive probability density. By determining Fisher information and Shannon entropy, we assess the sensitivity of probability distributions to parameter changes and the degree of uncertainty. Our research provides insights into the dynamics and information-theoretic characteristics of spin-0 particles in both spatial and momentum configurations. This work advances our understanding of the quantum information properties of spin-0 particles and lays the groundwork for future developments in quantum computing and information theory. Finally, the Stam, Cramer–Rao, and Bialynicki–Birula–Mycielski (BBM) inequalities have been verified, and we demonstrated that the BBM inequality remains valid in the form <span>\\\\(S_{x}+S_{p}\\\\ge 1+\\\\ln \\\\pi \\\\)</span>, consistent with ordinary quantum mechanics.</p>\",\"PeriodicalId\":597,\"journal\":{\"name\":\"International Journal of Theoretical Physics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2024-08-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Theoretical Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1007/s10773-024-05743-3\",\"RegionNum\":4,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"PHYSICS, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Theoretical Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1007/s10773-024-05743-3","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
Determination of Shannon entropy and Fisher information of the Feshbach-Villars oscillator for spin-0 particles
This paper is devoted to calculating the Fisher and Shannon information parameters of the Feshbach-Villars oscillator (FVO) for spin-0 particles. Instead of the Klein-Gordon equation, the Feshbach-Villars formalism provides a positive probability density. By determining Fisher information and Shannon entropy, we assess the sensitivity of probability distributions to parameter changes and the degree of uncertainty. Our research provides insights into the dynamics and information-theoretic characteristics of spin-0 particles in both spatial and momentum configurations. This work advances our understanding of the quantum information properties of spin-0 particles and lays the groundwork for future developments in quantum computing and information theory. Finally, the Stam, Cramer–Rao, and Bialynicki–Birula–Mycielski (BBM) inequalities have been verified, and we demonstrated that the BBM inequality remains valid in the form \(S_{x}+S_{p}\ge 1+\ln \pi \), consistent with ordinary quantum mechanics.
期刊介绍:
International Journal of Theoretical Physics publishes original research and reviews in theoretical physics and neighboring fields. Dedicated to the unification of the latest physics research, this journal seeks to map the direction of future research by original work in traditional physics like general relativity, quantum theory with relativistic quantum field theory,as used in particle physics, and by fresh inquiry into quantum measurement theory, and other similarly fundamental areas, e.g. quantum geometry and quantum logic, etc.