Non-perturbative formulation of resonant quantum mechanics within unified exact WKB framework

We study quasi-stationary states in quantum mechanics using the exact WKB analysis as a non-perturbative framework. We explore unstable states such as resonances by analyzing 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. A unified exact WKB framework is developed for exploring the equivalence and complementarity of different well-established regularizations \`a la Zel'dovich, complex scaling, and rigged Hilbert space within this framework.