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This is an unconventional review article on spectral problems in black hole perturbation theory. Our purpose is to explain how to apply various known techniques in quantum mechanics to such spectral problems. The article includes analytical/numerical treatments, semiclassical perturbation theory, the (uniform) WKB method and useful mathematical tools: Borel summations, Pad approximants, and so forth. The article is not comprehensive, but rather looks into a few examples from various points of view. The techniques in this article are widely applicable to many other examples.
Yasuyuki Hatsuda (Sat,) studied this question.