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Title: Анализ разделяющихся координат для свободного уравнения Клейна-Гордона
Other Titles: Analysis of devided coordinates for free Klein-Gordon equation
Authors: Гайдучик, А. В.
metadata.dc.contributor.advisor: Шаповалов, А. В.
Keywords: координаты; уравнение Клейна-Гордона; разделение переменных; методы разделения; переменные
Issue Date: 2018
Publisher: Издательский Дом Томского государственного университета
Citation: Гайдучик А. В. Анализ разделяющихся координат для свободного уравнения Клейна-Гордона / А. В. Гайдучик ; науч. рук. А. В. Шаповалов // Перспективы развития фундаментальных наук : сборник научных трудов XV Международной конференции студентов, аспирантов и молодых ученых, г. Томск, 24-27 апреля 2018 г. : в 7 т. — Томск : Издательский Дом Томского государственного университета, 2018. — Т. 1 : Физика. — [С. 87-89].
Abstract: In the present study, we examined the method of separation of variables in the Klein-Gordon equation, based on full sets of symmetry operators of equation, which was described in papers [1-4]. Separable coordinates presented were analyzed for verification of coordinate transformations with correct inverse formulas determined in the whole space domain of physical variables. Those coordinate systems which do not possess such transformations were modified and the problem of separation of variables was resolved for them. These coordinate systems were called "selected". Corresponding external electromagnetic fields, which admit separation of variables in the Klein - Gordon equation are presented in the selected coordinate systems. The modified coordinate systems form a two - parametric family. We show that the Maxwell equations for the admissible external fields do not depend on the parameters of coordinate systems. Moreover, we expect that the modified coordinate systems will allow us to examine the problem of completeness of solution basises in separable coordinates.
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