Speaker
Description
An attempt is made to unify the understanding of resonance phenomena, analytic spectra, and resurgence by developing and applying a mature exact-WKB framework. We begin by formulating non-perturbative resonances in quantum mechanics via the exact WKB method, demonstrated concretely in the inverted Rosen–Morse potential, where barrier resonances and quasi-stationary states are shown to match exact and WKB predictions. Next, we extend this framework to incorporate Zel’dovich regularization, complex scaling, and a modified rigged Hilbert space, thereby clarifying the equivalence and complementarity of these regularization methods and the functional analytic structure they define. Finally, we apply exact WKB and complex scaling to scattering problems, compute the continuum spectrum and the S-matrix, and reinterpret classical theorems such as Aguilar-Balslev-Combes and the Siegert boundary condition in this unified setting. The result is a coherent picture in which resonant poles, continuum spectra, and resurgent structures are seamlessly interconnected, giving new insight into the spectral theory of unstable quantum states.
