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pro vyhledávání: '"Turbiner, Alexander 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
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
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
Publikováno v:
J. Phys. B: At. Mol. Opt. Phys. 56 (2023) 165101 (9pp)
The analytic Born-Oppenheimer (B-O) potential curve for the ground state $X^1\Sigma^+$ of the molecule (H,D,T)Cl is constructed for the whole range of internuclear distances $R \in [0,\infty)$ with an accuracy of 3-5 figures in comparison with the RK
Externí odkaz:
http://arxiv.org/abs/2208.07895
Publikováno v:
Chemical Physics Letters 799 (2022) 139642
Following the first principles the analytic Born-Oppenheimer (BO) potential curve for the ground state $X^1\Sigma^+$ of the molecule ClF is proposed for whole range of internuclear distances $R \in [0,\infty)$. It is based on matching the perturbatio
Externí odkaz:
http://arxiv.org/abs/2202.10666
Publikováno v:
Acta Polytechnica 62(1): 208-210, 2022
It is already known that the quantum quartic single-well anharmonic oscillator $V_{ao}(x)=x^2+g^2 x^4$ and double-well anharmonic oscillator $V_{dw}(x)= x^2(1 - gx)^2$ are essentially one-parametric, their eigenstates depend on a combination $(g^2 \h
Externí odkaz:
http://arxiv.org/abs/2111.01546