Formulación espectral de Sturm-Liouville para los polinomios de Gegenbauer y su aplicación al potencial trigonométrico de Pöschl-Teller.
Saved in:
| Title: | Formulación espectral de Sturm-Liouville para los polinomios de Gegenbauer y su aplicación al potencial trigonométrico de Pöschl-Teller. |
|---|---|
| Authors: | Gómez-Hernández, José A.1 jgomez96@uasd.edu.do, Toribio-Milane, Juan1,2, Rosario-Roche, Pablo A.3, Salomón-Martínez, Samuel J.4 |
| Source: | Latin-American Journal of Physics Education. Mar2026, Vol. 20 Issue 1, p1-16. 16p. |
| Subject Terms: | Sturm-Liouville equation, Gegenbauer polynomials, Spectral theory, Hilbert space, Eigenvalues, Differential equations, Orthogonal polynomials |
| Abstract (English): | This paper studies a hypergeometric-type differential equation whose polynomial solutions give rise to the Gegenbauer polynomials. We develop a self-adjoint Sturm-Liouville formulation within a weighted Hilbert-space setting, which provides a natural route to orthogonality, norm formulas, and the associated spectral conditions. We also discuss symmetry and self-adjoint realizations of the differential operator under suitable endpoint conditions. As an application, we treat the trigonometric Pöschl-Teller well: through nondimensionalization, exact singularity extraction, and a change of variables, the model reduces directly to the Gegenbauer framework, yielding an explicit discrete spectrum and a closed family of normalized eigenfunctions. [ABSTRACT FROM AUTHOR] |
| Abstract (Spanish): | Este trabajo estudia la ecuación diferencial de tipo hipergeométrico que genera, como soluciones polinómicas, a los polinomios de Gegenbauer. Se presenta una formulación en forma autoadjunta de Sturm-Liouville y se establece el problema en un espacio de Hilbert con peso, lo que permite derivar de manera natural la ortogonalidad, las normas y las condiciones espectrales asociadas. Además, se analizan la simetría y las realizaciones autoadjuntas del operador diferencial mediante condiciones de frontera adecuadas. Como aplicación, se aborda el pozo trigonométrico de Pöschl-Teller: mediante escalamiento, extracción de singularidades y un cambio de variable, el problema se reduce directamente al modelo de Gegenbauer, obteniéndose un espectro discreto explícito y una familia cerrada de autofunciones normalizadas. [ABSTRACT FROM AUTHOR] |
| Copyright of Latin-American Journal of Physics Education is the property of Latin-American Physics Education Network and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Education Research Complete |
| FullText | Links: – Type: pdflink Text: Availability: 0 |
|---|---|
| Header | DbId: ehh DbLabel: Education Research Complete An: 194797893 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
| IllustrationInfo | |
| Items | – Name: Title Label: Title Group: Ti Data: Formulación espectral de Sturm-Liouville para los polinomios de Gegenbauer y su aplicación al potencial trigonométrico de Pöschl-Teller. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Gómez-Hernández%2C+José+A%2E%22">Gómez-Hernández, José A.</searchLink><relatesTo>1</relatesTo><i> jgomez96@uasd.edu.do</i><br /><searchLink fieldCode="AR" term="%22Toribio-Milane%2C+Juan%22">Toribio-Milane, Juan</searchLink><relatesTo>1,2</relatesTo><br /><searchLink fieldCode="AR" term="%22Rosario-Roche%2C+Pablo+A%2E%22">Rosario-Roche, Pablo A.</searchLink><relatesTo>3</relatesTo><br /><searchLink fieldCode="AR" term="%22Salomón-Martínez%2C+Samuel+J%2E%22">Salomón-Martínez, Samuel J.</searchLink><relatesTo>4</relatesTo> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Latin-American+Journal+of+Physics+Education%22">Latin-American Journal of Physics Education</searchLink>. Mar2026, Vol. 20 Issue 1, p1-16. 16p. – Name: Subject Label: Subject Terms Group: Su Data: <searchLink fieldCode="DE" term="%22Sturm-Liouville+equation%22">Sturm-Liouville equation</searchLink><br /><searchLink fieldCode="DE" term="%22Gegenbauer+polynomials%22">Gegenbauer polynomials</searchLink><br /><searchLink fieldCode="DE" term="%22Spectral+theory%22">Spectral theory</searchLink><br /><searchLink fieldCode="DE" term="%22Hilbert+space%22">Hilbert space</searchLink><br /><searchLink fieldCode="DE" term="%22Eigenvalues%22">Eigenvalues</searchLink><br /><searchLink fieldCode="DE" term="%22Differential+equations%22">Differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Orthogonal+polynomials%22">Orthogonal polynomials</searchLink> – Name: Abstract Label: Abstract (English) Group: Ab Data: This paper studies a hypergeometric-type differential equation whose polynomial solutions give rise to the Gegenbauer polynomials. We develop a self-adjoint Sturm-Liouville formulation within a weighted Hilbert-space setting, which provides a natural route to orthogonality, norm formulas, and the associated spectral conditions. We also discuss symmetry and self-adjoint realizations of the differential operator under suitable endpoint conditions. As an application, we treat the trigonometric Pöschl-Teller well: through nondimensionalization, exact singularity extraction, and a change of variables, the model reduces directly to the Gegenbauer framework, yielding an explicit discrete spectrum and a closed family of normalized eigenfunctions. [ABSTRACT FROM AUTHOR] – Name: Abstract Label: Abstract (Spanish) Group: Ab Data: Este trabajo estudia la ecuación diferencial de tipo hipergeométrico que genera, como soluciones polinómicas, a los polinomios de Gegenbauer. Se presenta una formulación en forma autoadjunta de Sturm-Liouville y se establece el problema en un espacio de Hilbert con peso, lo que permite derivar de manera natural la ortogonalidad, las normas y las condiciones espectrales asociadas. Además, se analizan la simetría y las realizaciones autoadjuntas del operador diferencial mediante condiciones de frontera adecuadas. Como aplicación, se aborda el pozo trigonométrico de Pöschl-Teller: mediante escalamiento, extracción de singularidades y un cambio de variable, el problema se reduce directamente al modelo de Gegenbauer, obteniéndose un espectro discreto explícito y una familia cerrada de autofunciones normalizadas. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Latin-American Journal of Physics Education is the property of Latin-American Physics Education Network and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=ehh&AN=194797893 |
| RecordInfo | BibRecord: BibEntity: Languages: – Code: spa Text: Spanish PhysicalDescription: Pagination: PageCount: 16 StartPage: 1 Subjects: – SubjectFull: Sturm-Liouville equation Type: general – SubjectFull: Gegenbauer polynomials Type: general – SubjectFull: Spectral theory Type: general – SubjectFull: Hilbert space Type: general – SubjectFull: Eigenvalues Type: general – SubjectFull: Differential equations Type: general – SubjectFull: Orthogonal polynomials Type: general Titles: – TitleFull: Formulación espectral de Sturm-Liouville para los polinomios de Gegenbauer y su aplicación al potencial trigonométrico de Pöschl-Teller. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Gómez-Hernández, José A. – PersonEntity: Name: NameFull: Toribio-Milane, Juan – PersonEntity: Name: NameFull: Rosario-Roche, Pablo A. – PersonEntity: Name: NameFull: Salomón-Martínez, Samuel J. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 03 Text: Mar2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 18709095 Numbering: – Type: volume Value: 20 – Type: issue Value: 1 Titles: – TitleFull: Latin-American Journal of Physics Education Type: main |
| ResultId | 1 |
