QUASI-EXACTLY SOLVABLE SCHRÖDINGER EQUATIONS, SYMMETRIC POLYNOMIALS AND FUNCTIONAL BETHE ANSATZ METHOD
dc.contributor.author | Quesne , Christiane | |
dc.date.accessioned | 2018-12-04T14:37:33Z | |
dc.date.available | 2018-12-04T14:37:33Z | |
dc.date.issued | 2018 | |
dc.identifier.citation | Acta Polytechnica. 2018, vol. 58, no. 2, p. 118-127. | |
dc.identifier.issn | 1210-2709 (print) | |
dc.identifier.issn | 1805-2363 (online) | |
dc.identifier.uri | http://hdl.handle.net/10467/79105 | |
dc.description.abstract | For applications to quasi-exactly solvable Schrödinger equations in quantum mechanics, we consider the general conditions that have to be satisfied by the coefficients of a second-order differential equation with at most k + 1 singular points in order that this equation has particular solutions that are nth-degree polynomials. In a first approach, we show that such conditions involve k - 2 integration constants, which satisfy a system of linear equations whose coefficients can be written in terms of elementary symmetric polynomials in the polynomial solution roots whenver such roots are all real and distinct. In a second approach, we consider the functional Bethe ansatz method in its most general form under the same assumption. Comparing the two approaches, we prove that the above-mentioned k - 2 integration constants can be expressed as linear combinations of monomial symmetric polynomials in the roots, associated with partitions into no more than two parts. We illustrate these results by considering a quasi-exactly solvable extension of the Mathews-Lakshmanan nonlinear oscillator corresponding to k = 4. | en |
dc.format.mimetype | application/pdf | |
dc.language.iso | eng | |
dc.publisher | České vysoké učení technické v Praze | cs |
dc.publisher | Czech Technical University in Prague | en |
dc.relation.ispartofseries | Acta Polytechnica | |
dc.relation.uri | https://ojs.cvut.cz/ojs/index.php/ap/article/view/4740 | |
dc.rights | Creative Commons Attribution 4.0 International License | en |
dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ | |
dc.subject | Schrödinger equation | en |
dc.subject | quasi-exactly solvable potentials | en |
dc.subject | symmetric polynomials | en |
dc.title | QUASI-EXACTLY SOLVABLE SCHRÖDINGER EQUATIONS, SYMMETRIC POLYNOMIALS AND FUNCTIONAL BETHE ANSATZ METHOD | |
dc.type | article | en |
dc.date.updated | 2018-12-04T14:37:33Z | |
dc.identifier.doi | 10.14311/AP.2018.58.0118 | |
dc.rights.access | openAccess | |
dc.type.status | Peer-reviewed | |
dc.type.version | publishedVersion |
Soubory tohoto záznamu
Tento záznam se objevuje v následujících kolekcích
Kromě případů, kde je uvedeno jinak, licence tohoto záznamu je Creative Commons Attribution 4.0 International License