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The eigenvalue problem for a perturbed two-dimensional resonant oscillator is considered. The exciting potential is given by a nonlocal nonlinearity of Hartree type with smooth self-action potential. To each representation… Click to show full abstract
The eigenvalue problem for a perturbed two-dimensional resonant oscillator is considered. The exciting potential is given by a nonlocal nonlinearity of Hartree type with smooth self-action potential. To each representation of the rotation algebra corresponds the spectral cluster around an energy level of the unperturbed operator. Asymptotic eigenvalues and asymptotic eigenfunctions close to the lower boundary of spectral clusters are obtained. For their calculation, asymptotic formulas for quantum means are used.
Journal Title: Mathematical Notes
Year Published: 2017
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