30 citations · 90 across the 14 of their papers we have counts for
14 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…
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…
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 $…
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…
SUSY Quantum Mechanics, (non)-Analyticity and Phase Transitions
Alexander V Turbiner
It is shown by analyzing the Schrödinger equation that discontinuities in the coupling constant can occur in both the energies and the eigenfunctions. Surprisingly, those disc…
Towards the "puzzle" of Chromium dimer Cr: predicting the Born-Oppenheimer rovibrational spectrum
Horacio Olivares-Pilón, Daniel Aguilar-Díaz, Alexander V. Turbiner
The experimentally-observed non-trivial electronic structure of the Cr dimer has made the calculation of its potential energy curve a theoretical challenge in the last decades.…
From quartic anharmonic oscillator to double well potential
Alexander V. Turbiner, J. C. del Valle
It is already known that the quantum quartic single-well anharmonic oscillator and double-well anharmonic oscillator are essentia…
Quantum and thermal fluctuations in quantum mechanics and field theories from a new version of semiclassical theory
M. A. Escobar-Ruiz, E. Shuryak, A. V. Turbiner
We develop a new semiclassical approach, which starts with the density matrix given by the Euclidean time path integral with fixed coinciding endpoints, and proceed by identifying…
Two charges on plane in a magnetic field I. "Quasi-equal" charges and neutral quantum system at rest cases
M. A. Escobar-Ruiz, A. V. Turbiner
Low-lying bound states for the problem of two Coulomb charges of finite masses on a plane subject to a constant magnetic field perpendicular to the plane are considered. Major…
Canonical Commutation Relation Preserving Maps
C. Chryssomalakos, A. Turbiner
We study maps preserving the Heisenberg commutation relation . We find a one-parameter deformation of the standard realization of the above algebra in terms of a coordin…
Quasi-Exactly-Solvable Many-Body Problems
A. Minzoni, M. Rosenbaum, A. Turbiner
Explicit examples of quasi-exactly-solvable -body problems on the line are presented. These are related to the hidden algebra , and they are of two types -- containing up…
On Polynomial Relations in the Heisenberg Algebra
N. Fleury, A. Turbiner
Polynomial relations between the generators of the classical and quantum Heisenberg algebras are presented. Some of those relations can have a meaning of the formulas of the normal…