Quantization of Action for Elementary Particles and the Principle of Least Action

Quantization of Action for Elementary Particles and the Principle of Least Action | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Physical Sciences - Article Quantization of Action for Elementary Particles and the Principle of Least Action Shuming Wen This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3896843/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract The uncertainty principle is a fundamental principle of quantum mechanics, but its exact mathematical expression cannot obtain correct results when used to solve theoretical problems such as the energy levels of hydrogen atoms, one-dimensional deep potential wells, one-dimensional harmonic oscillators, and double-slit experiments. Even after approximate treatment, the results obtained are not completely consistent with those obtained by solving Schrödinger’s equation. This indicates that further research on the uncertainty principle is necessary. Therefore, using the de Broglie matter wave hypothesis, we quantize the action of an elementary particle in natural coordinates and obtain the quantization condition and a new deterministic relation. Using this quantization condition, we obtain the energy level formulas of an elementary particle in different conditions in a classical way that is completely consistent with the results obtained by solving Schrödinger’s equation. A new physical interpretation is given for the particle eigenfunction independence of probability for an elementary particle: an elementary particle is in a particle state at the space-time point where the action is quantized, and in a wave state in the rest of the space-time region. The space-time points of particle nature and the wave regions of particle motion constitute the continuous trajectory of particle motion. When an elementary particle is in a particle state, it is localized, whereas in the wave state region, it is nonlocalized. Physical sciences/Physics/Quantum physics/Quantum mechanics Physical sciences/Mathematics and computing/Statistics elementary particle quantization of action deterministic relation inherent state nonprobabilistic interpretation localization region nonlocalization region Full Text Additional Declarations There is NO Competing Interest. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-3896843","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Physical Sciences - Article","associatedPublications":[],"authors":[{"id":269651556,"identity":"46c1098c-0356-40d7-b939-d8a7cf43ca45","order_by":0,"name":"Shuming Wen","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAq0lEQVRIiWNgGAWjYDACCTBpw8PP3kCaljQZyZ4DpGk5bGNww4FIHfKzu9MkPu44z8Nwg4Hxw8ccIrQY3Dm7TXLmmds8jLMbmCVnbiNGi0Tuttu8bbd5mGUOsDHzEqNFfgZQy9+2czxsEglEamG4AdTC2HaAh4doLQY3crf/7G1L5pHgOdhMnF+ADtts8LPNzt7+ePPBDx+JchgCMDaQpn4UjIJRMApGAW4AAHwTNln2YHFkAAAAAElFTkSuQmCC","orcid":"https://orcid.org/0000-0003-1523-1189","institution":"Kunming University of Science and Technology","correspondingAuthor":true,"prefix":"","firstName":"Shuming","middleName":"","lastName":"Wen","suffix":""}],"badges":[],"createdAt":"2024-01-25 10:40:23","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3896843/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3896843/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":50336432,"identity":"bb488b04-61b7-4ea5-831d-75aeb7b05c5a","added_by":"auto","created_at":"2024-01-30 02:30:30","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":416078,"visible":true,"origin":"","legend":"","description":"","filename":"ManuscriptQuantizationofActionforElementaryParticlesandthePrincipleofLeastAction.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3896843/v1_covered_ef4be50a-328a-45c1-9464-79f5aa3b3181.pdf"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Quantization of Action for Elementary Particles and the Principle of Least Action","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"elementary particle, quantization of action, deterministic relation, inherent state nonprobabilistic interpretation, localization region, nonlocalization region","lastPublishedDoi":"10.21203/rs.3.rs-3896843/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3896843/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe uncertainty principle is a fundamental principle of quantum mechanics, but its exact mathematical expression cannot obtain correct results when used to solve theoretical problems such as the energy levels of hydrogen atoms, one-dimensional deep potential wells, one-dimensional harmonic oscillators, and double-slit experiments. 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