The one-dimensional Coulomb Hamiltonian: Properties of its Birman-Schwinger operator

The one-dimensional Coulomb Hamiltonian: Properties of its Birman-Schwinger operator | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL Mathematical Methods in the Applied Sciences This is a preprint and has not been peer reviewed. Data may be preliminary. 29 January 2025 V1 Latest version Share on The one-dimensional Coulomb Hamiltonian: Properties of its Birman-Schwinger operator Authors : S. Fassari , Manuel Gadella 0000-0001-8860-990X , Jose T. Lunardi , Luis M. Nieto 0000-0002-2849-2647 [email protected] , and F. Rinaldi Authors Info & Affiliations https://doi.org/10.22541/au.173815322.29222127/v1 Published Mathematical Methods in the Applied Sciences Version of record Peer review timeline 359 views 182 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract We study the Birman-Schwinger operator for a self-adjoint realisation of the one-dimensional Hamiltonian with the Coulomb potential. We study both the case in which this Hamiltonian is defined on the whole real line and when it is only defined on the positive semiaxis. In both cases, the Birman-Schwinger operator is Hilbert-Schmidt, even though it is not trace class. Then, we have considered some approximations to the Hamiltonian depending on a positive parameter, under given conditions, and proved the convergence of the Birman-Schwinger operators of these approximations to the original Hamiltonian as the parameter goes to zero. Further comments and results have been included. Supplementary Material File (coulomb_may_12_2024.pdf) Download 333.19 KB Information & Authors Information Version history V1 Version 1 29 January 2025 Peer review timeline Published Mathematical Methods in the Applied Sciences Version of Record 27 Apr 2025 Published Copyright This work is licensed under a Non Exclusive No Reuse License. Collection Mathematical Methods in the Applied Sciences Keywords birman-schwinger principle coulomb potential hilbert-schmidt operators resolvent convergence Authors Affiliations S. Fassari Universita degli Studi Guglielmo Marconi Dipartimento di Scienze Ingegneristiche View all articles by this author Manuel Gadella 0000-0001-8860-990X Universidad de Valladolid View all articles by this author Jose T. Lunardi Universidade Estadual de Ponta Grossa View all articles by this author Luis M. Nieto 0000-0002-2849-2647 [email protected] Universidad de Valladolid View all articles by this author F. Rinaldi Universita degli Studi Guglielmo Marconi Dipartimento di Scienze Ingegneristiche View all articles by this author Metrics & Citations Metrics Article Usage 359 views 182 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation S. Fassari, Manuel Gadella, Jose T. Lunardi, et al. The one-dimensional Coulomb Hamiltonian: Properties of its Birman-Schwinger operator. Authorea . 29 January 2025. 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