161 citations · 305 across the 15 of their papers we have counts for
15 papers
Wolfes model aka -rational integrable model: hidden algebras and quartic polynomial algebra of integrals
J C Lopez Vieyra, A V Turbiner
One-dimensional 3-body Wolfes model with 2- and 3-body interactions also known as -rational integrable model of the Hamiltonian reduction is exactly-solvable and superinte…
Radial power-like potentials: from the Bohr-Sommerfeld -state energies to the exact ones
J. C. del Valle, A. V. Turbiner
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 -dimension…
Ultra-Compact accurate wave functions for He-like and Li-like iso-electronic sequences and variational calculus. III. Spin-quartet state of the Lithium sequence
D. J. Nader, J. C. del Valle, J. C. Lopez Vieyra +1
As a continuation of Part I, dedicated to the ground state of He-like and Li-like isoelectronic sequences for nuclear charges , and Part II, dedicated to two excited sta…
Ultra-Compact accurate wave functions for He-like and Li-like iso-electronic sequences and variational calculus. II. Spin-singlet (excited) and spin-triplet (lowest) states of the Helium sequence
A. V. Turbiner, J. C. Lopez Vieyra, J. C. del Valle +1
As a continuation of Part I \cite{Part-1:2020} (Int. Journal of Quantum Chem. 2021; 121: qua.26586), dedicated to the ground state of He-like and Li-like isoelectronic sequences fo…
Two-body neutral Coulomb system in a magnetic field at rest: from Hydrogen atom to positronium
J. C. del Valle, A. V. Turbiner, Adrian M Escobar Ruiz
A simple locally accurate uniform approximation for the nodeless wavefunction is constructed for a {\it neutral} system of two Coulomb charges of different masses and $(…
The molecule in a strong magnetic field revisited
D. J. Nader, A. V. Turbiner, J. C. López Vieyra
A compact, few-parametric, physically adequate, 3-term variational trial function is used to calculate with high accuracy the energy of the ground state of the hydrogen m…
The He molecular ion and the He atomic ion in strong magnetic fields
J. C. Lopez Vieyra, A. V. Turbiner
We study the question about existence i.e. stability with respect to dissociation of the spin-quartet, permutation- and reflection-symmetric () state…
Nuclear critical charge for two-electron ion in Lagrange mesh method
H. Olivares Pilón, A. V. Turbiner
The Schroedinger equation for two electrons in the field of a charged fixed center is solved with the Lagrange mesh method for charges close to the critical charge . We…
On 1/Z expansion for two-electron systems
J. C. Lopez Vieyra, A. V. Turbiner
The -expansion for the Coulomb system of infinitely massive center of charge Z and two electrons is discussed. Numerical deficiency in Baker et al, {\em Phys. Rev. \bf A41}, 1…
Two charges on a plane in a magnetic field: hidden algebra, (particular) integrability, polynomial eigenfunctions
A. V. Turbiner, M. A. Escobar-Ruiz
The quantum mechanics of two Coulomb charges on a plane and subject to a constant magnetic field perpendicular to the plane is considered. Four integr…
From Quantum (Calogero) to (Rational) Model
Alexander V. Turbiner
A brief and incomplete review of known integrable and (quasi)-exactly-solvable quantum models with rational (meromorphic in Cartesian coordinates) potentials is given. All of them…
Helium- and Lithium-like ionic sequences: Critical charges
N. L. Guevara, A. V. Turbiner
In non-relativistic quantum mechanics we study the Coulomb systems of infinitely massive center of charge Z and two-three electrons: and . It is shown that in…
An infinite family of solvable and integrable quantum systems on a plane
Frédérick Tremblay, Alexander V. Turbiner, Pavel Winternitz
An infinite family of exactly-solvable and integrable potentials on a plane is introduced. It is shown that all already known rational potentials with the above properties allowing…
H_3^{++}$ molecular ion in a strong magnetic field: triangular configuration
J. C. Lopez Vieyra, A. V. Turbiner
The existence of the molecular ion in a magnetic field in a triangular configuration is revised. Variational method with an optimization of the form of the vector potent…
H2+ ion in strong magnetic field: a variational study
J. C. Lopez, P. O. Hess, A. Turbiner
Using a single trial function we perform an accurate calculation of the ground state of the hydrogenic molecular ion in a constant uniform magnetic field ranging $0-…