Zobrazeno 1 - 10
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pro vyhledávání: '"Turbiner, A."'
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 that discontinuities in the coupling constant can occur in both the energies and the eigenfunctions. Surprisingly, those discontinuities, which are present in the energies {\it versus} the coup
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