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pro vyhledávání: '"Pogosyan, A. S."'
This monograph is the English version of the book "Quantum systems with hidden symmetry. Interbasis expansions" published in 2006 by the publishing house FIZMATLIT (Moscow) in Russian. When compiling this version of the book, typos and inaccuracies n
Externí odkaz:
http://arxiv.org/abs/2310.17336
Akademický článek
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Publikováno v:
Journal of Mathematical Physics 58, 103505 (2017)
The differential equation with free boundary conditions on the unit disk that was proposed by Frits Zernike in 1934 to find Jacobi polynomial solutions (indicated as I), serves to define a classical and a quantum system which have been found to be su
Externí odkaz:
http://arxiv.org/abs/1708.06666
The differential equation proposed by Frits Zernike to obtain a basis of polynomial orthogonal solutions on the the unit disk to classify wavefront aberrations in circular pupils, is shown to have a set of new orthonormal solution bases, involving Le
Externí odkaz:
http://arxiv.org/abs/1705.08482
Publikováno v:
Journal of Mathematical Physics 58, 072901 (2017)
We consider the differential equation that Zernike proposed to classify aberrations of wavefronts in a circular pupil, as if it were a classical Hamiltonian with a non-standard potential. The trajectories turn out to be closed ellipses. We show that
Externí odkaz:
http://arxiv.org/abs/1702.08566
Publikováno v:
Journal of Mathematical Physics 58, 072101 (2017)
We consider the differential equation that Zernike proposed to classify aberrations of wavefronts in a circular pupil, whose value at the boundary can be nonzero. On this account the quantum Zernike system, where that differential equation is seen as
Externí odkaz:
http://arxiv.org/abs/1702.08570
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 fi
Externí odkaz:
http://arxiv.org/abs/1603.08139
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 expansio
Externí odkaz:
http://arxiv.org/abs/1603.07971
Autor:
Pogosyan, G. S., Yakhno, A.
In this work the detailed geometrical description of all possible orthogonal and nonorthogonal systems of coordinates, which allow separation of variables of two-dimensional Helmholtz equation is given as for two-sheeted (upper sheet) $H_2$, either f
Externí odkaz:
http://arxiv.org/abs/1510.03785
Publikováno v:
SIGMA 11 (2015), 096, 23 pages
In the present work the classical problem of harmonic oscillator in the hyperbolic space $H_2^2$: $z_0^2+z_1^2-z_2^2-z_3^2=R^2$ has been completely solved in framework of Hamilton-Jacobi equation. We have shown that the harmonic oscillator on $H_2^2$
Externí odkaz:
http://arxiv.org/abs/1504.06228