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This allows us to perform exact discrete calculations.<\/jats:p>","DOI":"10.3390\/sym9100217","type":"journal-article","created":{"date-parts":[[2017,10,9]],"date-time":"2017-10-09T11:25:35Z","timestamp":1507548335000},"page":"217","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Exact Finite Differences. The Derivative on Non Uniformly Spaced Partitions"],"prefix":"10.3390","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8380-5888","authenticated-orcid":false,"given":"Armando","family":"Mart\u00ednez-P\u00e9rez","sequence":"first","affiliation":[{"name":"Physics Department, Cinvestav, Apdo. postal 14-740, 07300 Mexico City, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3122-0546","authenticated-orcid":false,"given":"Gabino","family":"Torres-Vega","sequence":"additional","affiliation":[{"name":"Physics Department, Cinvestav, Apdo. postal 14-740, 07300 Mexico City, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,10,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"583","DOI":"10.1007\/BF00715110","article-title":"Quantum mechanics in finite dimensions","volume":"6","author":"Santhanam","year":"1976","journal-title":"Found. 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General Principles of Quantum Mechanics, Springer.","DOI":"10.1007\/978-3-642-61840-6"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1365","DOI":"10.1139\/cjp-2016-0373","article-title":"Translations in quantum mechanics revisited. The point spectrum case","volume":"94","year":"2016","journal-title":"Can. J. Phys."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Gitman, D.M., Tyutin, I.V., and Voronov, B.L. (2012). Self-Adjoint Extensions in Quantum Mechanics. General Theory and Applications to Schr\u00f6dinger and Dirac Equations with Singular Potentials, Birkh\u00e4user.","DOI":"10.1007\/978-0-8176-4662-2"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Schm\u00fcdgen, K. (2012). Unbounded Self-Adjoint Operators on Hilbert Space, Springer.","DOI":"10.1007\/978-94-007-4753-1"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/9\/10\/217\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:46:44Z","timestamp":1760208404000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/9\/10\/217"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,10,7]]},"references-count":12,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2017,10]]}},"alternative-id":["sym9100217"],"URL":"https:\/\/doi.org\/10.3390\/sym9100217","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2017,10,7]]}}}