arXiv subjects

Juan C. Lopez Vieyra

Publications and source records attributed to Juan C. Lopez Vieyra.

3 recordsLinked to original sources

arXiv2017

Helium-like and Lithium-like ions: Ground state energy

It is shown that the non-relativistic ground state energy of helium-like and lithium-like ions with static nuclei can be interpolated in full physics range of nuclear charges $Z$ with accuracy of not less than 6 decimal digits (d.d.) or 7-8 significant digits (s.d.) using a meromorphic function in appropriate variable with a few free parameters. It is demonstrated that finite nuclear mass effects do not change 4-5 s.d. for $Z \in [1,50]$ for 2-,3-electron systems and the leading relativistic and QED corrections leave unchanged 3-4 s.d. for $Z \in [1,12]$ in the ground state energy for 2-electron system, thus, the interpolation reproduces definitely those figures. A meaning of proposed interpolation is in a construction of unified, {\it two-point} Pade approximant (for both small and large $Z$ expansions) with fitting some parameters at intermediate $Z$.

physics.atom-ph↗

arXiv2005

Solvability of the Hamiltonians related to exceptional root spaces: rational case

Solvability of the rational quantum integrable systems related to exceptional root spaces $G_2, F_4$ is re-examined and for $E_{6,7,8}$ is established in the framework of a unified approach. It is shown the Hamiltonians take algebraic form being written in a certain Weyl-invariant variables. It is demonstrated that for each Hamiltonian the finite-dimensional invariant subspaces are made from polynomials and they form an infinite flag. A notion of minimal flag is introduced and minimal flag for each Hamiltonian is found. Corresponding eigenvalues are calculated explicitly while the eigenfunctions can be computed by pure linear algebra means for {\it arbitrary} values of the coupling constants. The Hamiltonian of each model can be expressed in the algebraic form as a second degree polynomial in the generators of some infinite-dimensional but finitely-generated Lie algebra of differential operators, taken in a finite-dimensional representation.

hep-th↗

arXiv2003

Solvability of $F_4$ quantum integrable systems

It is shown that the $F_4$ rational and trigonometric integrable systems are exactly-solvable for {\it arbitrary} values of the coupling constants. Their spectra are found explicitly while eigenfunctions are obtained by pure algebraic means. For both systems new variables are introduced in which the Hamiltonian has an algebraic form being also (block)-triangular. These variables are a certain invariants of the $F_4$ Weyl group. Both Hamiltonians preserve the same (minimal) flag of spaces of polynomials, which is found explicitly.

math-ph↗