Quasimodes and exponential splitting of eigenvalues. (Russian) Zbl 0599.47033

An abstract theorem is proved which permits the determination of eigenvalues of a self-adjoint operator starting from its quasi- eigenvalues. With the help of this theorem expressions are derived for an exponentially small splitting of energy levels in the Schrödinger equation with a smooth, not necessarily even, potential in the case of two mirror-symmetric potential wells and in the case of a finite number of equal potential wells.
Reviewer: O.Dumbrajs


47B25 Linear symmetric and selfadjoint operators (unbounded)
47A10 Spectrum, resolvent
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics