SWKB quantization condition for conditionally exactly solvable systems and the residual corrections
The SWKB quantization condition is an exact quantization condition for the conventional shape-invariant potentials. On the other hand, this condition equation does not hold for other known solvable systems. The origin of the (non-)exactness is understood in the context of the quantum Hamilton–Jacobi...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2023-02-01
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| Series: | Nuclear Physics B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0550321323000160 |
| _version_ | 1797897311070715904 |
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| author | Yuta Nasuda Nobuyuki Sawado |
| author_facet | Yuta Nasuda Nobuyuki Sawado |
| author_sort | Yuta Nasuda |
| collection | DOAJ |
| description | The SWKB quantization condition is an exact quantization condition for the conventional shape-invariant potentials. On the other hand, this condition equation does not hold for other known solvable systems. The origin of the (non-)exactness is understood in the context of the quantum Hamilton–Jacobi formalism. First we confirm the statement and show inexplicit properties numerically for the case of the conditionally exactly solvable systems by Junker and Roy. The SWKB condition clearly breaks for this case, but the condition equation is restored within a certain degree of accuracy. We propose a novel approach to evaluate the residual by perturbation, intending to explore what the correction terms for the SWKB condition equation look like. |
| first_indexed | 2024-04-10T07:56:33Z |
| format | Article |
| id | doaj.art-9013d5c7626249a5a7477c5c2bc7b359 |
| institution | Directory Open Access Journal |
| issn | 0550-3213 |
| language | English |
| last_indexed | 2024-04-10T07:56:33Z |
| publishDate | 2023-02-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Nuclear Physics B |
| spelling | doaj.art-9013d5c7626249a5a7477c5c2bc7b3592023-02-23T04:30:04ZengElsevierNuclear Physics B0550-32132023-02-01987116087SWKB quantization condition for conditionally exactly solvable systems and the residual correctionsYuta Nasuda0Nobuyuki Sawado1Corresponding author.; Department of Physics, Graduate School of Science and Technology, Tokyo University of Science, Noda, Chiba 278-8510, JapanDepartment of Physics, Graduate School of Science and Technology, Tokyo University of Science, Noda, Chiba 278-8510, JapanThe SWKB quantization condition is an exact quantization condition for the conventional shape-invariant potentials. On the other hand, this condition equation does not hold for other known solvable systems. The origin of the (non-)exactness is understood in the context of the quantum Hamilton–Jacobi formalism. First we confirm the statement and show inexplicit properties numerically for the case of the conditionally exactly solvable systems by Junker and Roy. The SWKB condition clearly breaks for this case, but the condition equation is restored within a certain degree of accuracy. We propose a novel approach to evaluate the residual by perturbation, intending to explore what the correction terms for the SWKB condition equation look like.http://www.sciencedirect.com/science/article/pii/S0550321323000160 |
| spellingShingle | Yuta Nasuda Nobuyuki Sawado SWKB quantization condition for conditionally exactly solvable systems and the residual corrections Nuclear Physics B |
| title | SWKB quantization condition for conditionally exactly solvable systems and the residual corrections |
| title_full | SWKB quantization condition for conditionally exactly solvable systems and the residual corrections |
| title_fullStr | SWKB quantization condition for conditionally exactly solvable systems and the residual corrections |
| title_full_unstemmed | SWKB quantization condition for conditionally exactly solvable systems and the residual corrections |
| title_short | SWKB quantization condition for conditionally exactly solvable systems and the residual corrections |
| title_sort | swkb quantization condition for conditionally exactly solvable systems and the residual corrections |
| url | http://www.sciencedirect.com/science/article/pii/S0550321323000160 |
| work_keys_str_mv | AT yutanasuda swkbquantizationconditionforconditionallyexactlysolvablesystemsandtheresidualcorrections AT nobuyukisawado swkbquantizationconditionforconditionallyexactlysolvablesystemsandtheresidualcorrections |