arXiv subjects
Publications and source records attributed to V. S. Otchik.
The classical Kepler-Coulomb problem on the single-sheeted hyperboloid $H^{3}_1$ is solved in the framework of the Hamilton--Jacobi equation. We have proven that all the bounded orbits are closed and periodic. The paths are ellipses or circles for finite motion.
Eigenfunctions of the Schrodinger equation with the Coulomb potential in the imaginary Lobachevsky space are studied in two coordinate systems admitting solutions in terms of hypergeometric functions. Normalization and coefficients of mutual expansions for some sets of solutions are found.
5-Dimensional wave equation for a massive particle of spin 1 in the background of de Sitter space-time model is solved in static coordinates. The spherical 5-dimensional vectors $A_{a}, a= 1,...,5$ of three types, $j,j+1, j-1$ are constructed. In massless case they give electromagnetic wave solutions, obeying the Lorentz condition. 5-form of equations in massless case is used to produce recipe to build electromagnetic wave solutions of the types $Π, E,M$; the first is trivial and can be removed by a gauge ransformation. The recipe is specified to produce spherical $Π, E, M$ solutions in static coordinates.
By analogy with the Lobachevsky space H_{3}, generalized parabolic coordinates (t_{1},t_{2},ϕ) are introduced in Riemannian space model of positive constant curvature S_{3}. In this case parabolic coordinates turn out to be complex valued and obey additional restrictions involving the complex conjugation. In that complex coordinate system, the quantum-mechanical Coulomb problem is stu- died: separation of variables is carried out and the wave solutions in terms of hypergeometric functions are obtained. At separating the variables, two parameters k_{1} and k_{2} are introduced, and an operator B with the eigen values (k_{1}+k_{2}) is found, which is related to third component of the known Runge-Lenz vector in space S_{3} as follows: i B = A _{3} + i \vec{L}^{2}, whereas in the Lobachevsky space as B =A_{3} + \vec{L}^{2}. General aspects of the possibility to employ complex coordinate systems in the real space model S_{3} are discussed.