Abstract:
In the eigenvalue problem for a perturbed two-dimensional
oscillator, we suggest a method for constructing asymptotic solutions
near the boundaries of spectral clusters by means of a new integral
representation and study the issue of calculating the average values
of differential operators on the solutions near the boundaries of the
clusters.
Keywords:operator averaging method, coherent transform, WKB-approximation,
turning point, spectral cluster.
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