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Non-perturbative formulation of resonances in quantum mechanics based on exact WKB method (2503.18741v2)
Published 24 Mar 2025 in hep-th, nucl-th, and quant-ph
Abstract: We study quasi-stationary states in quantum mechanics using the exact WKB analysis as a non-perturbative framework. While previous works focus 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 non-polynomial potentials.