Asymptotics of the spectrum and quantum averages of a perturbed resonant oscillator near the boundaries of spectral clusters

作者：Pereskokov A V^*

来源：Izvestiya - Mathematics, 2013, 77(1): 163-210.

DOI：10.1070/IM2013v077n01ABEH002632

• operator averaging method
• coherent transform
• WKB-approximation
• turning point
• spectral cluster

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.

• 出版日期2013