Papers by George Pogosyan
Physica Scripta, 2019
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Journal of the Optical Society of America A, 2017
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ABSTRACT
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Theoretical and Mathematical Physics
We construct a complex transformation $$S_{1\mathbb{C}} \to S_1 $$ generalizing the known Hurwitz... more We construct a complex transformation $$S_{1\mathbb{C}} \to S_1 $$ generalizing the known Hurwitz transformation in the Euclidean space for one-dimensional quantum mechanics. As in the case of the flat space, this transformation allows establishing the connection between the Coulomb problem and the oscillator problem with the Calogero–Sutherland potential added. We fully describe the motion in a Coulomb field in S1 and determine the energy spectrum and the wave functions with the correct normalizing constant.
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Algebraic Methods in Physics, 2001
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Теоретическая и математическая физика, 2001
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Physics of Atomic Nuclei, 2007
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Physics of Atomic Nuclei, 2008
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Physics of Atomic Nuclei, 2005
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Theoretical and Mathematical Physics - THEOR MATH PHYS-ENGL TR, 2001
We show that Graf's addition theorem for Bessel functions is obtained by contraction of the ... more We show that Graf's addition theorem for Bessel functions is obtained by contraction of the composition formula for SO(3) rotations.
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Journal of Physics A: Mathematical and General, 1999
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Journal of Physics A: Mathematical and General, 1997
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Journal of Physics A: Mathematical and General, 1983
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In this article we show that separation of variables for second-order superintegrable systems in ... more In this article we show that separation of variables for second-order superintegrable systems in two-dimensional Euclidean space generates both exactly solvable (ES) and quasi-exactly solvable (QES) problems in quantum mechanics. In this article we propose the another definition of ES and QES. The quantum mechanical problem is called ES if the solution of Schroedinger equation, can be expressed in terms of hypergeometrical functions $_mF_n$ and is QES if the Schroedinger equation admit polynomial solutions with the coefficients satisfying the three-term or more higher order of recurrence relations
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Physics of Particles and Nuclei, 2007
In this paper, the Feynman path integral technique is applied for superintegrable potentials on t... more In this paper, the Feynman path integral technique is applied for superintegrable potentials on two-dimensional spaces of nonconstant curvature: these spaces are Darboux spaces D I and D II. On D I, there are three, and on D II four such potentials. We are able to evaluate the path integral in most of the separating coordinate systems, leading to expressions for the Green functions, the discrete and continuous wave-functions, and the discrete energy-spectra. In some cases, however, the discrete spectrum cannot be stated explicitly, because it is either determined by a transcendental equation involving parabolic cylinder functions (Darboux space I), or by a higher order polynomial equation. The solutions on D I in particular show that superintegrable systems are not necessarily degenerate. We can also show how the limiting cases of flat space (constant curvature zero) and the two-dimensional hyperboloid (constant negative curvature) emerge.
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It is shown, that oscillators on the sphere and the pseudosphere are related, by the so-called Bo... more It is shown, that oscillators on the sphere and the pseudosphere are related, by the so-called Bohlin transformation, with the Coulomb systems on the pseudosphere. The even states of an oscillator yield the conventional Coulomb system on the pseudosphere, while the odd states yield the Coulomb system on the pseudosphere in the presence of magnetic flux tube generating spin 1/2. A similar relation is established for the oscillator on the (pseudo)sphere specified by the presence of constant uniform magnetic field $B_0$ and the Coulomb-like system on pseudosphere specified by the presence of the magnetic field $\frac{B}{2r_0}(|\frac{x_3}{{\bf x}}|-\epsilon)$. The correspondence between the oscillator and the Coulomb systems the higher dimensions is also discussed.
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Physics of Atomic Nuclei, Mar 1, 2010
The Inönü-Wigner contraction from the SO(2, 1) group to the Euclidean E(2) and E(1, 1) group is u... more The Inönü-Wigner contraction from the SO(2, 1) group to the Euclidean E(2) and E(1, 1) group is used to relate the separation of variables in Laplace-Beltrami (Helmholtz) equations for the four corresponding two-dimensional homogeneous spaces: two-dimensional hyperboloids and two-dimensional Euclidean and pseudo-Euclidean spaces. We show how the nine systems of coordinates on the two-dimensional hyperboloids contracted to the four systems of coordinates on E 2 and eight on E 1,1. The text was submitted by the authors in English.
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Papers by George Pogosyan