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The general goal of my work is to construct an asymptotic solution to the spectral problem for the one-dimensional Shrodinger equation with a potential having a localized perturbation near the fixed point. We consider the spectral problem in the semiclassical limit. The potential has the form of an asymmetric potential well with a barrier. When the width of this barrier changes, which means a change in a small parameter, both the form of solution and the geometric objects that are used to construct the solution change.