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arXiv · 2503.18741

Nonperturbative Formulation of Resonances in Quantum Mechanics Based on Exact WKB Method

Okuto Morikawa·Shoya Ogawa
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Abstract

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.

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Okuto Morikawa, Shoya Ogawa. 2025-03-24. Nonperturbative Formulation of Resonances in Quantum Mechanics Based on Exact WKB Method. https://doi.org/10.1093/ptep%2Fptaf120

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