Nonperturbative Formulation of Resonances in Quantum Mechanics Based on Exact WKB Method
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911209736896512 |
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| author | Morikawa, Okuto Ogawa, Shoya |
| author_facet | Morikawa, Okuto Ogawa, Shoya |
| contents | We study quasi-stationary states in quantum mechanics using the exact Wentzel--Kramers--Brillouin (WKB) analysis as a nonperturbative framework. Whereas previous works focused mainly on stable systems, we explore unstable states such as resonances. As a concrete example, we analyze the inverted Rosen--Morse potential, which exhibits barrier resonance. This model allows exact solutions, enabling a direct comparison with exact WKB predictions. We provide a simple analytic picture of resonance and demonstrate consistency between exact and WKB-based results, extending the applicability of exact WKB analysis to nonpolynomial potentials. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_18741 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonperturbative Formulation of Resonances in Quantum Mechanics Based on Exact WKB Method Morikawa, Okuto Ogawa, Shoya High Energy Physics - Theory Nuclear Theory Quantum Physics We study quasi-stationary states in quantum mechanics using the exact Wentzel--Kramers--Brillouin (WKB) analysis as a nonperturbative framework. Whereas previous works focused mainly on stable systems, we explore unstable states such as resonances. As a concrete example, we analyze the inverted Rosen--Morse potential, which exhibits barrier resonance. This model allows exact solutions, enabling a direct comparison with exact WKB predictions. We provide a simple analytic picture of resonance and demonstrate consistency between exact and WKB-based results, extending the applicability of exact WKB analysis to nonpolynomial potentials. |
| title | Nonperturbative Formulation of Resonances in Quantum Mechanics Based on Exact WKB Method |
| topic | High Energy Physics - Theory Nuclear Theory Quantum Physics |
| url | https://arxiv.org/abs/2503.18741 |