Unification and extension of the factorization method for constructing exactly and conditionally-exactly solvable potentials. The case of a single potential generating function
The article proposes a new algorithm for applying the factorization method to the problem of calculating the spectrum of exactly and conditionally exactly solvable potentials. The proposed algorithm allows us to unify and extend the capabilities of the factorization method to construct exactly solva...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2022-10-01
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| Series: | Results in Physics |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2211379722005642 |
| _version_ | 1798001394101256192 |
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| author | R.R. Nigmatullin A.A. Khamzin D. Baleanu |
| author_facet | R.R. Nigmatullin A.A. Khamzin D. Baleanu |
| author_sort | R.R. Nigmatullin |
| collection | DOAJ |
| description | The article proposes a new algorithm for applying the factorization method to the problem of calculating the spectrum of exactly and conditionally exactly solvable potentials. The proposed algorithm allows us to unify and extend the capabilities of the factorization method to construct exactly solvable potentials. The new approach is demonstrated by calculating the eigenvalues of exactly solvable potentials constructed using a single function in the form of the Laurent-type polynomial. The algorithm makes it possible to significantly simplify the scheme for calculating the spectrum, parameters of the superpotential, as well as the constrain conditions for the parameters of the potential, in the case of conditionally exactly solvable potentials. It is shown that the shape of the spectrum is determined only by the differential equation, which is satisfied by the potential generating function. |
| first_indexed | 2024-04-11T11:36:38Z |
| format | Article |
| id | doaj.art-47c96808e3e04c5aa716e2e8a7294d9a |
| institution | Directory Open Access Journal |
| issn | 2211-3797 |
| language | English |
| last_indexed | 2024-04-11T11:36:38Z |
| publishDate | 2022-10-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Physics |
| spelling | doaj.art-47c96808e3e04c5aa716e2e8a7294d9a2022-12-22T04:25:57ZengElsevierResults in Physics2211-37972022-10-0141105945Unification and extension of the factorization method for constructing exactly and conditionally-exactly solvable potentials. The case of a single potential generating functionR.R. Nigmatullin0A.A. Khamzin1D. Baleanu2Kazan National Research Technical University Named After A.N. Tupolev - KAI, Radioelectronics and Informative Measurements Technics Department, K. Marx Str. 10, 420111, Kazan, RussiaKazan Federal University, Institute of Physics, 420008, Kremlevskaya Str. 18, Kazan, RussiaCankaya University, Faculty of Arts and Sciences, Department of Mathematics, 06530, Ankara, Turkey; Institute of Space Sciences, P.O. Box, MG-23, R 76900, Magurele-Bucharest, Romania; Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan; Corresponding author.The article proposes a new algorithm for applying the factorization method to the problem of calculating the spectrum of exactly and conditionally exactly solvable potentials. The proposed algorithm allows us to unify and extend the capabilities of the factorization method to construct exactly solvable potentials. The new approach is demonstrated by calculating the eigenvalues of exactly solvable potentials constructed using a single function in the form of the Laurent-type polynomial. The algorithm makes it possible to significantly simplify the scheme for calculating the spectrum, parameters of the superpotential, as well as the constrain conditions for the parameters of the potential, in the case of conditionally exactly solvable potentials. It is shown that the shape of the spectrum is determined only by the differential equation, which is satisfied by the potential generating function.http://www.sciencedirect.com/science/article/pii/S2211379722005642 |
| spellingShingle | R.R. Nigmatullin A.A. Khamzin D. Baleanu Unification and extension of the factorization method for constructing exactly and conditionally-exactly solvable potentials. The case of a single potential generating function Results in Physics |
| title | Unification and extension of the factorization method for constructing exactly and conditionally-exactly solvable potentials. The case of a single potential generating function |
| title_full | Unification and extension of the factorization method for constructing exactly and conditionally-exactly solvable potentials. The case of a single potential generating function |
| title_fullStr | Unification and extension of the factorization method for constructing exactly and conditionally-exactly solvable potentials. The case of a single potential generating function |
| title_full_unstemmed | Unification and extension of the factorization method for constructing exactly and conditionally-exactly solvable potentials. The case of a single potential generating function |
| title_short | Unification and extension of the factorization method for constructing exactly and conditionally-exactly solvable potentials. The case of a single potential generating function |
| title_sort | unification and extension of the factorization method for constructing exactly and conditionally exactly solvable potentials the case of a single potential generating function |
| url | http://www.sciencedirect.com/science/article/pii/S2211379722005642 |
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