[1711.10322] Bound states of the $D$-dimensional Schrödinger equation for the generalized Woods-Saxon potential Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Nuclear Theory arXiv:1711.10322 (nucl-th) [Submitted on 24 Nov 2017] Title: Bound states of the $D$-dimensional Schrödinger equation for the generalized Woods-Saxon potential Authors: V. H. Badalov , B. Baris , K. Uzun View a PDF of the paper titled Bound states of the $D$-dimensional Schr\"{o}dinger equation for the generalized Woods-Saxon potential, by V. H. Badalov and 1 other authors View PDF HTML (experimental) Abstract: In this paper, the approximate analitical solutions of the hyper-radial Schrödinger equation are obtained for the generalized Wood-Saxon potential by implementing the Pekeris approximation to surmount the centrifugal term. The energy eigenvalues and corresponding hyper-radial wave functions are found for any angular momentum case via the Nikiforov-Uvarov (NU) and Supersymmetric quantum mechanics (SUSY QM) methods. Hence, the same expressions are obtained for the energy eigenvalues, and the expression of hyper-radial wave functions transformed each other is shown owing to these methods. Furthermore, a finite number energy spectrum depending on the depths of the potential well $V_{0}$ and $W$, the radial $n_{r}$ and $l$ orbital quantum numbers and parameters $D,a,R_{0}$ are also identified in detail. Finally, the bound state energies and the corresponding normalized hyper-radial wave functions for the neutron system of the a $^{56} Fe$ nucleus are calculated in $D=2$ and $D=3$, as well as the energy spectrum expressions of other highest dimensions are identified by using the energy spectrum of $D=2$ and $D=3$. Comments: 24 pages, 2 fugures, 2 tables. arXiv admin note: text overlap with arXiv:1501.02948 by other authors Subjects: Nuclear Theory (nucl-th) ; Mathematical Physics (math-ph) Cite as: arXiv:1711.10322 [nucl-th] (or arXiv:1711.10322v1 [nucl-th] for this version) https://doi.org/10.48550/arXiv.1711.10322 Focus to learn more arXiv-issued DOI via DataCite Related DOI : https://doi.org/10.1142/S0217732319501074 Focus to learn more DOI(s) linking to related resources Submission history From: Vatan Badalov [ view email ] [v1] Fri, 24 Nov 2017 06:10:53 UTC (39 KB) Full-text links: Access Paper: View a PDF of the paper titled Bound states of the $D$-dimensional Schr\"{o}dinger equation for the generalized Woods-Saxon potential, by V. H. Badalov and 1 other authors View PDF HTML (experimental) TeX Source view license Current browse context: nucl-th < prev | next > new | recent | 2017-11 Change to browse by: math math-ph math.MP References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from