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The hydrogen atom with the Coulomb interaction is one of the exactly solvable non-relativistic quantum models. Unlike many other exactly solvable models it describes a real physical object providing the formulas for energy levels and…
The quantum description of a particle moving in a deformed potential is investigated. A pseudostate (PS) basis is used to represent the states of the composite system. This PS basis is obtained by diagonalizing the system Hamiltonian in a…
A rapid and relatively simple scheme of calculation is elaborated and applied to cosmological recombination of helium. Employing the nonrelativistic Coulomb Green's function, a wavefunction of a colliding electron is represented in an…
We implement the rotationally-invariant formulation of the two-dimensional Hubbard model, with nearest-neighbors hopping $t$, which allows for the analytical study of the system in the low-energy limit. Both U(1) and SU(2) gauge…
We present an efficient numerical method for simulating the low-energy properties of disordered many-particle systems. The method which is based on the quantum-chemical configuration interaction approach consists in diagonalizing the…
We scrutinize the behavior of eigenvalues of an electron of Helium atom as it interacts with electric field directed along $z$-axis and exposed to linearly polarized intense laser field radiation. In order to achieve this, we freeze one…
The oscillator parameter in nuclei is refitted to reproduce the available charge radius data. As an important improvement, we include the Coulomb term evaluated within the assumption of a uniformly charged sphere, and take into account the…
We study the Hartree model for two electrons with spin, living in the two-dimensional or three-dimensional space with Coulomb interactions and submitted to the potential induced by two nuclei of charge +1. In the limit where the nuclei move…
The relation between certain Hamiltonians, known as dual, or partner Hamiltonians, under the transformation $x{\rightarrow}\bar{x}^{\bar{\alpha}}$ has long been used as a method of simplifying spectral problems in quantum mechanics. This…
Using the approach the modified Euler-Lagrange field equation together with the corresponding Seiberg-Witten maps of the dynamical fields, a noncommutative Dirac equation with a Coulomb potential is derived. We then find the noncommutative…
The two-electron problem for the helium-like atom/ions in $S$-state is considered. The basis containing the integer powers of $\ln r$, where $r$ is a radial variable of the Fock expansion, is studied. In this basis, the analytic expressions…
We present a detailed formalism of the microscopic particle-rotor model for hypernuclear low-lying states based on a covariant density functional theory. In this method, the hypernuclear states are constructed by coupling a hyperon to…
A new variational basis with well-behaved local approximation properties and multiple output is proposed for Coulomb systems. The trial function has proper behaviour at all Coulomb centres. Nonlinear asymptotic parameters are introduced…
A hyperbolic singularity in the wave-function of $s$-wave interacting atoms is the root problem for any accurate numerical simulation. Here we apply the transcorrelated method, whereby the wave-function singularity is explicitly described…
Some relevant transport properties of solids do not depend only on the spectrum of the electronic Hamiltonian, but on finer properties preserved only by unitary equivalence, the most striking example being the conductance. When interested…
Quantum-mechanical system -- spin 1 particle in external Coulomb field is studied on the base of the matrix Duffin-Kemmer-Petiau formalism with the use of the tetrad technique. Separation of the variables is performed with the help of…
A representation of polymer self-consistent field theory equivalent to quantum density functional theory is given in terms of non-orthogonal basis sets. Molecular integrals and self-consistent equations for spherically symmetric systems…
The energy levels of hydrogen and helium atoms in strong magnetic fields are calculated in this study. The current work contains estimates of the binding energies of the first few low-lying states of these systems that are improvements upon…
The diagonalization of the metrical Hamiltonian of a scalar field with an arbitrary coupling with a curvature in N-dimensional homogeneous isotropic space is performed. The energy spectrum of the corresponding quasiparticles is obtained.…
By deriving the 3/2 dimensional Hamiltonian equations for electrons in the intense laser radiation and quasi-static transverse electric and longitudinal magnetic fields, the electron heating mechanisms are examined both for low harmonic…