7 papers
Helium-like ions in Lagrange Mesh method, interpolating the highly-accurate energy spectra vs. Z
H Olivares-Pilon, JC Lopez-Vieyra, AV Turbiner
Two alternative approaches for studying Helium-like atomic ions in non-relativistic quantum mechanics are proposed: (I) a numerical approach, based on the Lagrange-mesh method whic…
Potential Energy Curves of Hydrogenic Halides HX(F,Cl,Br) and i-DMFT Method
H Olivares Pilon, A V Turbiner
A comparison of the {\it ab initio} calculations using the i-DMFT Method by Di Liu et al. (2025) with benchmark potential curves for three HX(F,Cl,Br) halides shows their inaccurac…
Quantum two-dimensional superintegrable systems in flat space: exact-solvability, hidden algebra, polynomial algebra of integrals
Alexander V Turbiner, Juan Carlos Lopez Vieyra, Pavel Winternitz
In this short review paper the detailed analysis of six two-dimensional quantum {\it superintegrable} systems in flat space is presented. It includes the Smorodinsky-Winternitz pot…
Tremblay-Turbiner-Winternitz (TTW) system at integer index : polynomial algebras of integrals
Juan Carlos López Vieyra, Alexander V Turbiner
An infinite 3-parametric family of superintegrable and exactly-solvable quantum models on a plane, admitting separation of variables in polar coordinates, marked by integer index $…
On the spectral theory in the Fock space with polynomial eigenfunctions
A. V. Turbiner, N. L. Vasilevski
The notion of the eigenvalue problem in the Fock space with polynomial eigenfunctions is introduced. This problem is classified by using the finite-dimensional representations of t…
The ground electronic state of CS: the potential curve and associated Born-Oppenheimer rovibrational spectrum
Horacio Olivares-Pilon, Alexander V Turbiner
Basics of the Born-Oppenheimer (B-O) approximation are reviewed. Assuming the domain of applicability of B-O approximation is limited to 4 significant digits (s.d.) in energy spect…