A Look at the Measurement of the Quantum Wave function

A Look at the Measurement of the Quantum Wave function | 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Download PDF Article A Look at the Measurement of the Quantum Wave function Daniel McKeown This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-2571455/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 In Non-Relativistic Quantum Mechanics, the Schr¨odinger equation describes the evolution of a quantum system as a superposition of different states, but cannot explain why the system is only ever measured to be in one of these states. Here we show a new dynamical wave equation for the evolution of the wave function, and then apply this equation to a variety of different physical cases, showing how the wave function changes when we move from one potential to another. We then show how a measurement in quantum mechanics is an example of a potential changing the possible eigenvalues associated with a quantum system. The dynamical process of a measurement that evolves the wave function not only returns a single eigenvalue for the basis it is measuring, but also returns a new Hamiltonian with corresponding eigenvalues. This shows, contrary to some interpretations, that the wave function is continuous after measurement. Physical sciences/Physics/Quantum physics/Quantum mechanics Physical sciences/Physics/Quantum physics/Quantum simulation 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. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-2571455","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":175674312,"identity":"08668f45-ee14-46bd-8653-4424ab26cd82","order_by":0,"name":"Daniel McKeown","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAsElEQVRIiWNgGAWjYDCCAwzMYJofzIZyiNMi2UCyFoMDYIoILXzXDj82+FBxOM/4RvLDAwwV1okNhLRI3k4zTpxx5nCx2Y00oEVn0glrMbidw3yYt+124rYbOQwHGNsOE6nlL1DL5hkgLf+I1JLMCNSyQQKkpYEILSC/GPac+Q/0zzODAwnH0o0JauG7nfxY4kdFWmJ/e/LjDx9qrGUJakEFCaQpHwWjYBSMglGACwAAgW1Hf1VmYiEAAAAASUVORK5CYII=","orcid":"https://orcid.org/0000-0002-5121-7117","institution":"University of California Irvine","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Daniel","middleName":"","lastName":"McKeown","suffix":""}],"badges":[],"createdAt":"2023-02-10 06:20:45","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-2571455/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-2571455/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":33507023,"identity":"8a61ab15-eafc-4174-84d0-dfe0bc7a98e6","added_by":"auto","created_at":"2023-02-27 15:41:25","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":627768,"visible":true,"origin":"","legend":"Article File","description":"","filename":"DanielMcKeown2023.pdf","url":"https://assets-eu.researchsquare.com/files/rs-2571455/v1_covered.pdf"},{"id":33195558,"identity":"bfef1edd-55bf-4d51-b665-5897745a662a","added_by":"auto","created_at":"2023-02-20 19:58:59","extension":"pdf","order_by":11,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1059687,"visible":true,"origin":"","legend":"","description":"","filename":"DanielMcKeown2023.pdf","url":"https://assets-eu.researchsquare.com/files/rs-2571455/v1/4c8eeaf3ec3b00fd161fd86b.pdf"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"A Look at the Measurement of the Quantum Wave function","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":"","lastPublishedDoi":"10.21203/rs.3.rs-2571455/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-2571455/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"In Non-Relativistic Quantum Mechanics, the Schr¨odinger equation describes the evolution of a\r\nquantum system as a superposition of different states, but cannot explain why the system is only\r\never measured to be in one of these states. 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