Unified Algorithm of Factorization Method for Derivation of Exact Solutions from Schrödinger Equation with Potentials Constructed from a Set of Functions
We extend the scope of the unified factorization method to the solution of conditionally and unconditionally exactly solvable models of quantum mechanics, proposed in a previous paper [R.R. Nigmatullin, A.A. Khamzin, D. Baleanu, <i>Results in Physics</i> 41 (2022) 105945]. The possibilit...
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| Format: | Article |
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MDPI AG
2023-09-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/18/3822 |
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| author | Raoul R. Nigmatullin Airat A. Khamzin |
| author_facet | Raoul R. Nigmatullin Airat A. Khamzin |
| author_sort | Raoul R. Nigmatullin |
| collection | DOAJ |
| description | We extend the scope of the unified factorization method to the solution of conditionally and unconditionally exactly solvable models of quantum mechanics, proposed in a previous paper [R.R. Nigmatullin, A.A. Khamzin, D. Baleanu, <i>Results in Physics</i> 41 (2022) 105945]. The possibilities of applying the unified approach in the factorization method are demonstrated by calculating the energy spectrum of a potential constructed in the form of a second-order polynomial in many of the linearly independent functions. We analyze the solutions in detail when the potential is constructed from two linearly independent functions. We show that in the general case, such kinds of potentials are conditionally exactly solvable. To verify the novel approach, we consider several known potentials. We show that the shape of the energy spectrum is invariant to the number of functions from which the potential is formed and is determined by the type of differential equations that the potential-generating functions obey. |
| first_indexed | 2024-03-10T22:30:10Z |
| format | Article |
| id | doaj.art-91e315a893d446a19e5819fdb5c35a42 |
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| language | English |
| last_indexed | 2024-03-10T22:30:10Z |
| publishDate | 2023-09-01 |
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| spelling | doaj.art-91e315a893d446a19e5819fdb5c35a422023-11-19T11:48:05ZengMDPI AGMathematics2227-73902023-09-011118382210.3390/math11183822Unified Algorithm of Factorization Method for Derivation of Exact Solutions from Schrödinger Equation with Potentials Constructed from a Set of FunctionsRaoul R. Nigmatullin0Airat A. Khamzin1Radioelectronics and Informative Measurements Technics Department, Kazan National Research Technical University Named after A.N. Tupolev—KAI, K. Marx Str. 10, 420111 Kazan, RussiaInstitute of Physics, Kazan Federal University, Kremlevskaya Str. 18, 420008 Kazan, RussiaWe extend the scope of the unified factorization method to the solution of conditionally and unconditionally exactly solvable models of quantum mechanics, proposed in a previous paper [R.R. Nigmatullin, A.A. Khamzin, D. Baleanu, <i>Results in Physics</i> 41 (2022) 105945]. The possibilities of applying the unified approach in the factorization method are demonstrated by calculating the energy spectrum of a potential constructed in the form of a second-order polynomial in many of the linearly independent functions. We analyze the solutions in detail when the potential is constructed from two linearly independent functions. We show that in the general case, such kinds of potentials are conditionally exactly solvable. To verify the novel approach, we consider several known potentials. We show that the shape of the energy spectrum is invariant to the number of functions from which the potential is formed and is determined by the type of differential equations that the potential-generating functions obey.https://www.mdpi.com/2227-7390/11/18/3822exactly solvable modelsconditionally exactly solvable modelsSchrödinger equationfactorization methodsuperpotential |
| spellingShingle | Raoul R. Nigmatullin Airat A. Khamzin Unified Algorithm of Factorization Method for Derivation of Exact Solutions from Schrödinger Equation with Potentials Constructed from a Set of Functions Mathematics exactly solvable models conditionally exactly solvable models Schrödinger equation factorization method superpotential |
| title | Unified Algorithm of Factorization Method for Derivation of Exact Solutions from Schrödinger Equation with Potentials Constructed from a Set of Functions |
| title_full | Unified Algorithm of Factorization Method for Derivation of Exact Solutions from Schrödinger Equation with Potentials Constructed from a Set of Functions |
| title_fullStr | Unified Algorithm of Factorization Method for Derivation of Exact Solutions from Schrödinger Equation with Potentials Constructed from a Set of Functions |
| title_full_unstemmed | Unified Algorithm of Factorization Method for Derivation of Exact Solutions from Schrödinger Equation with Potentials Constructed from a Set of Functions |
| title_short | Unified Algorithm of Factorization Method for Derivation of Exact Solutions from Schrödinger Equation with Potentials Constructed from a Set of Functions |
| title_sort | unified algorithm of factorization method for derivation of exact solutions from schrodinger equation with potentials constructed from a set of functions |
| topic | exactly solvable models conditionally exactly solvable models Schrödinger equation factorization method superpotential |
| url | https://www.mdpi.com/2227-7390/11/18/3822 |
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