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Article

О туннельном возмущении дискретного спектра

We conceder  semiclassical asymptotics of the energy levels shift of the  Schrödinger operator discrete spectrum with a one-dimensional single-well potential that appears due to a deformation of the potential in the classically forbidden region. Since such a deformation of the potential effects on the quantum particle only due to the tunneling effects, then the corresponding shift of the energy levels is exponentially small. We obtain asymptotic semiclassical formulas for the shift of the energy levels for various types of the potential deformation.