The evolution operator of the Hartree-type equation with a quadratic potential / A. L. Lisok, A. Yu. Trifonov, A. V. Shapovalov

Уровень набора: Journal of Physics A: Mathematical and General, Scientific JournalОсновной Автор-лицо: Lisok, A. L., physicist, Associate Professor of Tomsk Polytechnic University, Candidate of physical and mathematical sciences, 1981-, Aleksandr LeonidovichАльтернативный автор-лицо: Trifonov, A. Yu., physicist, mathematician, Professor of Tomsk Polytechnic University, Doctor of physical and mathematical sciences, 1963-, Andrey Yurievich;Shapovalov, A. V., mathematician, Professor of Tomsk Polytechnic University, Doctor of physical and mathematical sciences, 1949-, Aleksandr VasilyevichЯзык: английский.Страна: .Резюме или реферат: Based on the ideology of the Maslov complex germ theory, a method has been developed for finding an exact solution of the Cauchy problem for a Hartree-type equation with a quadratic potential in the class of semiclassically concentrated functions. The nonlinear evolution operator has been obtained in explicit form in the class of semiclassically concentrated functions. Parametric families of symmetry operators have been found for the Hartree-type equation. With the help of symmetry operators, families of exact solutions of the equation have been constructed. Exact expressions are obtained for the quasi-energies and their respective states. The Aharonov–Anandan geometric phases are found in explicit form for the quasi-energy states.Примечания о наличии в документе библиографии/указателя: [References: 26 tit.].Аудитория: .Тематика: электронный ресурс | труды учёных ТПУ Ресурсы он-лайн:Щелкните здесь для доступа в онлайн
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[References: 26 tit.]

Based on the ideology of the Maslov complex germ theory, a method has been developed for finding an exact solution of the Cauchy problem for a Hartree-type equation with a quadratic potential in the class of semiclassically concentrated functions. The nonlinear evolution operator has been obtained in explicit form in the class of semiclassically concentrated functions. Parametric families of symmetry operators have been found for the Hartree-type equation. With the help of symmetry operators, families of exact solutions of the equation have been constructed. Exact expressions are obtained for the quasi-energies and their respective states. The Aharonov–Anandan geometric phases are found in explicit form for the quasi-energy states

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