Abstract
Two coupled anharmonic oscillators are considered as a model for a nonperturbative description of the correlation and nonadiabatic effects which are typical for many-dimensional quantum systems. The eigenvalues and eigenfunctions for this model are found by means of the operator method, modified for the case of degenerate solutions of the Schr?dinger equation. It is shown that the zeroth approximation of the method allows one to find the analytical and uniformly suitable approximation for the energy levels and their splitting in the entire range of Hamiltonian parameters and quantum numbers. Numerical calculations demonstrate the convergence of the successive approximations, even for quasistationary states of the system. The results are of interest for applied problems of spectroscopy and solid state physics.
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