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pro vyhledávání: '"Turbiner, A. V."'
It is shown that for carbon monosulfide ${\rm C}\,{\rm S}$ in the Born-Oppenheimer formalism, by taking into account the RKR turning points found by Coxon and Hajigeorgiou (2023), and asymptotics at small and large internuclear distances, the potenti
Externí odkaz:
http://arxiv.org/abs/2409.14875
Autor:
Turbiner, Alexander V
It is shown by analyzing the $1D$ Schr\"odinger equation the discontinuities in the coupling constant can occur in both the energies and the eigenfunctions. Surprisingly, those discontinuities, which are present in the energies versus the coupling co
Externí odkaz:
http://arxiv.org/abs/2409.03081
The experimentally-observed non-trivial electronic structure of the Cr$_2$ dimer has made the calculation of its potential energy curve a theoretical challenge in the last decades. By matching the perturbation theory at small internuclear distances $
Externí odkaz:
http://arxiv.org/abs/2401.03259
Autor:
Vieyra, J C Lopez, Turbiner, A V
Publikováno v:
J. Math. Phys. 65, 051702 (2024)
One-dimensional 3-body Wolfes model with 2- and 3-body interactions also known as $G_2/I_6$-rational integrable model of the Hamiltonian reduction is exactly-solvable and superintegrable. Its Hamiltonian $H$ and two integrals ${\cal I}_{1}, {\cal I}_
Externí odkaz:
http://arxiv.org/abs/2310.20481
Publikováno v:
J.Phys.: Conference Series, 2667 (2023) 012075
It is shown that the two-body Coulomb problem in the Sturm representation leads to a new two-dimensional, exactly-solvable, superintegrable quantum system in curved space with a $g^{(2)}$ hidden algebra and a cubic polynomial algebra of integrals. Th
Externí odkaz:
http://arxiv.org/abs/2309.16886
Autor:
Vieyra, J. C. Lopez, Turbiner, A. V.
Publikováno v:
Advances in Quantum Chemistry 89 (2023) Chapter 5, 305-339
As a continuation of Parts I \cite{Part-1:2020}, II \cite{Part-2:2021}, III \cite{Part-3:2022}, where ultra-compact wave functions were constructed for a few low-lying states of He-like and Li-like sequences, the family of spin-singlet $(1s\,ns)$ typ
Externí odkaz:
http://arxiv.org/abs/2309.01292
Autor:
del Valle, J. C., Turbiner, A. V.
Publikováno v:
Int.Journ.Mod.Phys. A38, No.17 (2023) 2350092
Following our previous study of the Bohr-Sommerfeld (B-S) quantization condition for one-dimensional case (del Valle \& Turbiner (2021) \cite{First}), we extend it to $d$-dimensional power-like radial potentials. The B-S quantization condition for $S
Externí odkaz:
http://arxiv.org/abs/2305.11363
Publikováno v:
SIGMA 20 (2024), 012, 23 pages
It is shown that the $\mathfrak{gl}(3)$ polynomial integrable system, introduced by Sokolov-Turbiner in [arXiv:1409.7439], is equivalent to the $\mathfrak{gl}(3)$ quantum Euler-Arnold top in a constant magnetic field. Their Hamiltonian as well as the
Externí odkaz:
http://arxiv.org/abs/2305.00529
Publikováno v:
Phys Lett A 468 (2023) 128738
Taking the Hydrogen atom as an example it is shown that if the symmetry of a three-dimensional system is $O(2) \oplus Z_2$, the variables $(r, \rho, \varphi)$ allow a separation of the variable $\varphi$, and the eigenfunctions define a new family of
Externí odkaz:
http://arxiv.org/abs/2212.03108
Publikováno v:
Int J Mod Phys A 37 (34) (2022) 2250209
It is evident that the positions of 4 bodies in $d>2$ dimensional space can be identified with vertices of a tetrahedron. Square of volume of the tetrahedron, weighted sum of squared areas of four facets and weighted sum of squared edges are called t
Externí odkaz:
http://arxiv.org/abs/2209.01165