Related papers: Relativistic Coulomb Problem: Analytic Upper Bound…
By extending the concept of Euler-angle rotations to more than three dimensions, we develop the systematics under rotations in higher-dimensional space for a novel set of hyperspherical harmonics. Applying this formalism, we determine all…
We consider non-relativistic systems in quantum mechanics interacting through the Coulomb potential, and discuss the existence of bound states which are stable against spontaneous dissociation into smaller atoms or ions. We review the…
In the paper, the contact - boundary value problem with non-classical conditions not requiring agreement conditions is considered for a pseudoparabolic equation. The equivalence of these conditions is substantiated in the case if the…
The Dirac equation for the Coulomb problem is restated by incorporating a nonlinear effective interaction into the Dirac Hamiltonian: one keeps the $1/r$ dependence for the Coulomb field, but the coupling constant is modified by a factor…
It is known that binding energies calculated from the Bethe-Salpeter equation in ladder approximation can be reasonably well accounted for by an energy-dependent interaction, at least for the lowest states. It is also known that none of…
A special relativistic perturbation to non-relativistic quantum mechanics is shown to lead to the special relativistic prediction for the rate of precession for quantum states in the Coulomb potential. This behavior is shown using SO(4)…
Exact solutions of two-particle relativistic equations of quantum field theory describing the scattering $s$-states and the bound $s$-states are found in the cases of delta-shell potential and superposition of delta-shell potentials. Some…
Universal properties of the Coulomb interaction energy apply to all many-electron systems. Bounds on the exchange-correlation energy, inparticular, are important for the construction of improved density functionals. Here we investigate one…
In quantum systems with short-range interactions, causality imposes nontrivial constraints on low-energy scattering parameters. We investigate these causality constraints for systems where a long-range Coulomb potential is present in…
We study the lowest energy E of a relativistic system of N identical bosons bound by harmonic-oscillator pair potentials in three spatial dimensions. In natural units the system has the semirelativistic ``spinless-Salpeter'' Hamiltonian H =…
The model under consideration is a semi-infinite two-dimensional two-component plasma (Coulomb gas), stable against bulk collapse for the dimensionless coupling constant $\beta<2$, in contact with a dielectric wall of dielectric constant…
The quantum statistical treatment of the Rutherford model, considering matter as a system of point charges (electrons and nuclei) is analyzed. First, in the historical context, the solutions of different fundamental problems, such as the…
The explicit semiclassical treatment of the logarithmic perturbation theory for the bound-state problem of the radial Shrodinger equation with the screened Coulomb potential is developed. Based upon h-expansions and new quantization…
Relativistic correction to the Coulomb interaction is considered for strongly correlated electron orbitals. The atomic representation of the Coulomb-Breit interaction and its physical origin are clarified, to generalize a concept of the…
We have developed a field theory for strongly coupled Coulomb fluids, via introducing new functional--integral transformation of the electrostatic interaction energy. Our formalism not only reproduces the Lieb--Narnhofer lower bound, but…
The spatially-dependent mass Dirac equation is solved exactly for attractive scalar and repulsive vector Coulomb potentials including a tensor interaction potential under the spin and pseudospin (p-spin) symmetric limits by using the…
We show that there exist some intimate connections between three unconventional Schr\"odinger equations based on the use of deformed canonical commutation relations, of a position-dependent effective mass or of a curved space, respectively.…
The dynamics of relativistic (scalar and vector) bosons through nonminimal vector square (well and barrier) potentials is studied in the Duffin-Kemmer-Petiau (DKP) formalism. We show that the problem can be mapped in effective Schrodinger…
The Coulomb problem for vector bosons W incorporates a well known difficulty; the charge of the boson localized in a close vicinity of the attractive Coulomb center proves be infinite. This fact contradicts the renormalizability of the…
We investigate and prove Lieb-Oxford bounds in one dimension by studying convex potentials that approximate the ill-defined Coulomb potential. A Lieb-Oxford inequality establishes a bound of the indirect interaction energy for electrons in…