Exact solutions for time-dependent complex symmetric potential well
Using the pseudo-invariant operator method, we investigate the model of a particle with a time-dependent mass in a complex time-dependent symmetric potential well V (x, t) = if (t) |x|. The problem is exactly solvable and the analytic expressions of the Schrödinger wavefunctions are given in terms o...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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CTU Central Library
2023-05-01
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| Series: | Acta Polytechnica |
| Subjects: | |
| Online Access: | https://ojs.cvut.cz/ojs/index.php/ap/article/view/8348 |
| _version_ | 1827953560120197120 |
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| author | Boubakeur Khantoul Abdelhafid Bounames |
| author_facet | Boubakeur Khantoul Abdelhafid Bounames |
| author_sort | Boubakeur Khantoul |
| collection | DOAJ |
| description | Using the pseudo-invariant operator method, we investigate the model of a particle with a time-dependent mass in a complex time-dependent symmetric potential well V (x, t) = if (t) |x|. The problem is exactly solvable and the analytic expressions of the Schrödinger wavefunctions are given in terms of the Airy function. Indeed, with an appropriate choice of the time-dependent metric operators and the unitary transformations, for each region, the two corresponding pseudo-Hermitian invariants transform into a well-known time-independent Hermitian invariant which is the Hamiltonian of a particle confined in a symmetric linear potential well. The eigenfunctions of the last invariant are the Airy functions. Then, the phases obtained are real for both regions and the general solution to the problem is deduced. |
| first_indexed | 2024-04-09T14:16:40Z |
| format | Article |
| id | doaj.art-c2083c0dbb004caf944338efed8fb385 |
| institution | Directory Open Access Journal |
| issn | 1805-2363 |
| language | English |
| last_indexed | 2024-04-09T14:16:40Z |
| publishDate | 2023-05-01 |
| publisher | CTU Central Library |
| record_format | Article |
| series | Acta Polytechnica |
| spelling | doaj.art-c2083c0dbb004caf944338efed8fb3852023-05-05T09:41:31ZengCTU Central LibraryActa Polytechnica1805-23632023-05-0163213213910.14311/AP.2023.63.01325588Exact solutions for time-dependent complex symmetric potential wellBoubakeur Khantoul0https://orcid.org/0000-0001-9012-4864Abdelhafid Bounames1https://orcid.org/0000-0002-5998-2710University of Jijel, Department of Physics, Laboratory of Theoretical Physics, BP 98 Ouled Aissa, 18000 Jijel, Algeria; University of Constantine 3 – Salah Boubnider University, Department of Process Engineering, BP B72 Ali Mendjeli, 25000 Constantine, AlgeriaUniversity of Jijel, Department of Physics, Laboratory of Theoretical Physics, BP 98 Ouled Aissa, 18000 Jijel, AlgeriaUsing the pseudo-invariant operator method, we investigate the model of a particle with a time-dependent mass in a complex time-dependent symmetric potential well V (x, t) = if (t) |x|. The problem is exactly solvable and the analytic expressions of the Schrödinger wavefunctions are given in terms of the Airy function. Indeed, with an appropriate choice of the time-dependent metric operators and the unitary transformations, for each region, the two corresponding pseudo-Hermitian invariants transform into a well-known time-independent Hermitian invariant which is the Hamiltonian of a particle confined in a symmetric linear potential well. The eigenfunctions of the last invariant are the Airy functions. Then, the phases obtained are real for both regions and the general solution to the problem is deduced.https://ojs.cvut.cz/ojs/index.php/ap/article/view/8348non-hermitian hamiltoniantime-dependent hamiltonianpseudo-invariant methodpt-symmetrypseudo-hermiticity |
| spellingShingle | Boubakeur Khantoul Abdelhafid Bounames Exact solutions for time-dependent complex symmetric potential well Acta Polytechnica non-hermitian hamiltonian time-dependent hamiltonian pseudo-invariant method pt-symmetry pseudo-hermiticity |
| title | Exact solutions for time-dependent complex symmetric potential well |
| title_full | Exact solutions for time-dependent complex symmetric potential well |
| title_fullStr | Exact solutions for time-dependent complex symmetric potential well |
| title_full_unstemmed | Exact solutions for time-dependent complex symmetric potential well |
| title_short | Exact solutions for time-dependent complex symmetric potential well |
| title_sort | exact solutions for time dependent complex symmetric potential well |
| topic | non-hermitian hamiltonian time-dependent hamiltonian pseudo-invariant method pt-symmetry pseudo-hermiticity |
| url | https://ojs.cvut.cz/ojs/index.php/ap/article/view/8348 |
| work_keys_str_mv | AT boubakeurkhantoul exactsolutionsfortimedependentcomplexsymmetricpotentialwell AT abdelhafidbounames exactsolutionsfortimedependentcomplexsymmetricpotentialwell |