{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:50:02Z","timestamp":1760233802518,"version":"build-2065373602"},"reference-count":38,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2021,2,21]],"date-time":"2021-02-21T00:00:00Z","timestamp":1613865600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We find supersymmetric partners of a family of self-adjoint operators which are self-adjoint extensions of the differential operator \u2212d2\/dx2 on L2[\u2212a,a], a&gt;0, that is, the one dimensional infinite square well. First of all, we classify these self-adjoint extensions in terms of several choices of the parameters determining each of the extensions. There are essentially two big groups of extensions. In one, the ground state has strictly positive energy. On the other, either the ground state has zero or negative energy. In the present paper, we show that each of the extensions belonging to the first group (energy of ground state strictly positive) has an infinite sequence of supersymmetric partners, such that the \u2113-th order partner differs in one energy level from both the (\u2113\u22121)-th and the (\u2113+1)-th order partners. In general, the eigenvalues for each of the self-adjoint extensions of \u2212d2\/dx2 come from a transcendental equation and are all infinite. For the case under our study, we determine the eigenvalues, which are also infinite, all the extensions have a purely discrete spectrum, and their respective eigenfunctions for all of its \u2113-th supersymmetric partners of each extension.<\/jats:p>","DOI":"10.3390\/sym13020350","type":"journal-article","created":{"date-parts":[[2021,2,21]],"date-time":"2021-02-21T23:59:31Z","timestamp":1613951971000},"page":"350","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Supersymmetric Partners of the One-Dimensional Infinite Square Well Hamiltonian"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8860-990X","authenticated-orcid":false,"given":"Manuel","family":"Gadella","sequence":"first","affiliation":[{"name":"Departamento de F\u00edsica Te\u00f3rica, At\u00f3mica y \u00d3ptica and IMUVA, Universidad de Valladolid, 47011 Valladolid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0072-6077","authenticated-orcid":false,"given":"Jos\u00e9","family":"Hern\u00e1ndez-Mu\u00f1oz","sequence":"additional","affiliation":[{"name":"Departamento de F\u00edsica Te\u00f3rica de la Materia Condensada, IFIMAC Condensed Matter Physics Center, Universidad Aut\u00f3noma de Madrid, 28049 Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2849-2647","authenticated-orcid":false,"given":"Luis Miguel","family":"Nieto","sequence":"additional","affiliation":[{"name":"Departamento de F\u00edsica Te\u00f3rica, At\u00f3mica y \u00d3ptica and IMUVA, Universidad de Valladolid, 47011 Valladolid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7506-5552","authenticated-orcid":false,"given":"Carlos","family":"San Mill\u00e1n","sequence":"additional","affiliation":[{"name":"Departamento de F\u00edsica Te\u00f3rica, At\u00f3mica y \u00d3ptica and IMUVA, Universidad de Valladolid, 47011 Valladolid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,2,21]]},"reference":[{"key":"ref_1","first-page":"3","article-title":"Supersymmetric quantum mechanics","volume":"1287","year":"2010","journal-title":"AIP Conf. 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