Numerical method for solving Schrödinger equations using wavelet basis functions

Numerical method for solving Schrödinger equations using wavelet basis functions | 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 Research Article Numerical method for solving Schrödinger equations using wavelet basis functions Myoung Won Cho This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6195274/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 9 You are reading this latest preprint version Abstract This paper presents a numerical method for solving Schrödinger equations with arbitrary potentials with the adoption of the qunatum diagonalization scheme and basis functions in the discrete wavelet transform. The quantum diagonalization scheme, developed to solve the Hubbard model and so on, is known to allow the diagonalization of a Hamiltonian matrix of a much large size because it does not require to maintain the entire matrix in memory. And, the adoption of wavelet basis functions enables representing eigenstates efficiently using a number of bases much smaller than the number of grid points to integral and reducing the computation time to perform the diagonalization process. With the help of another additional techniques, the method allows to find solutions of a Schrödinger equation much exactly and efficiently. The validity of the method and its efficiency depending on several conditions are proven and surveyed by applying it to several problems for which the exact solutions are known. Schrödinger equation quantum diagonalization wavelet Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 20 Jul, 2025 Reviews received at journal 17 Jul, 2025 Reviews received at journal 17 Jul, 2025 Reviewers agreed at journal 28 Jun, 2025 Reviewers agreed at journal 26 Jun, 2025 Reviewers invited by journal 26 Jun, 2025 Editor assigned by journal 16 Mar, 2025 Submission checks completed at journal 14 Mar, 2025 First submitted to journal 10 Mar, 2025 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. 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