Related papers: Bounds on Diatomic Molecules in a Relativistic Mod…
Paralleling a previous paper, we examine single- and many-body states of relativistic electrons in an intense, rotating magnetic dipole field. Single-body orbitals are derived semiclassically and then applied to the many-body case via the…
Various models of charged particles interacting with a quantized, ultraviolet cutoff radiation field (but not with each other) are investigated. Upper and lower bounds are found for the self- or ground state-energies without mass…
In this work, the hydrogen's ionization energy was used to constrain the free parameter $b$ of three Born-Infeld-like electrodynamics namely Born-Infeld itself, Logarithmic electrodynamics and Exponential electrodynamics. An analytical…
With recent developments in simulating nonadiabatic systems to high accuracy, it has become possible to determine how much energy is attributed to nuclear quantum effects beyond zero-point energy. In this work we calculate the…
Proposed is system of consistent mathematical models describing physical laws of a system of energy emitting bodies in dynamics, relativity and nuclear physics. It is shown the use of developed models for the description of systems,…
The well known relation of Einstein relativistic energy for a free particle is extended to cover the total relativistic energy of a bound particle by calculating the relativistic potential energy. A non dissipative harmonic oscillator…
We develop a model of molecular binding based on the Bohr-Sommerfeld description of atoms together with a constraint taken from conventional quantum mechanics. The model can describe the binding energy curves of H2, H3 and other molecules…
The ground states of N-electron parabolic quantum dots in the presence of a perpendicular magnetic field are investigated. Rigorous lower bounds to the ground-state energies are obtained. It is shown that our lower bounds agree well with…
We present the construction of an exponentially accurate time-dependent Born-Oppenheimer approximation for molecular quantum mechanics. We study molecular systems whose electron masses are held fixed and whose nuclear masses are…
Simple analytic formulae for energy relaxation (ER) in electron-ion systems, with quantum corrections, ion dynamics and RPA-type screening are presented. ER in the presence of bound electrons is examined in view of of recent simulations for…
The spectral properties of up to four interacting electrons confined within a quasi one--dimensional system of finite length are determined by numerical diagonalization including the spin degree of freedom. The ground state energy is…
The relativistic ``no pair'' model of quantum electrodynamics uses the Dirac operator, D(A), for the electron dynamics together with the usual self-energy of the quantized ultraviolet cutoff electromagnetic field A -- in the Coulomb gauge.…
Based on a simplest molecular orbital theory of H$_{2}^{+}$, a three-parameter model potential function is proposed to describe ground-state diatomic systems with closed-shell and/or S-type valence-shell constituents over a significantly…
The total energies of a large number of diatomic (or two-center) one-electron $A^{+} B^{+} e^{-}$ ions with unit electrical charges are determined numerically to high accuracy. Based on these results we derive some accurate…
We study systems containing electrons and nuclei. Based on the fact that the thermodynamic limit exists for systems with Dirichlet boundary conditions, we prove that the same limit is obtained if one imposes other boundary conditions such…
Theoretical and experimental values to date for the resistances of single molecules commonly disagree by orders of magnitude. By reformulating the transport problem using boundary conditions suitable for correlated many-electron systems, we…
Spectroscopic techniques are very essential tools in studying electronic structures, spectroscopic constants and energetic properties of diatomic molecules. These techniques are also required for parametrization of new method based on…
Bounds on the exchange-correlation energy of many-electron systems are derived and tested. By using universal scaling properties of the electron-electron interaction, we obtain the exponent of the bounds in three, two, one, and quasi-one…
We substantiate the need for account of the proper electromagnetic field of the electron in the canonical problem of hydrogen in relativistic quantum mechanics. From mathematical viewpoint, the goal is equivalent to determination of the…
The energy method can be used to identify well-posed initial boundary value problems for quasi-linear, symmetric hyperbolic partial differential equations with maximally dissipative boundary conditions. A similar analysis of the discrete…