Related papers: Atomic H over plane: effective potential and level…
Energy spectrums of a nonrelativistic particle and an H-like atom in a spherical box of size R with general conditions of "not going out" through the box surface are explored. The lowest energy levels reconstruction is described from the…
The physical origin is investigated of Robin boundary conditions for wave functions at an infinite reflecting wall. We consider both Schr\"odinger and phase-space quantum mechanics (a.k.a. deformation quantization), for this simple example…
In this paper, we consider the problem of nonlinear (in particular, saturated) stabilization of the high-dimensional wave equation with Dirichlet boundary conditions. The wave dynamics are subject to a dissipative nonlinear velocity…
In this article, we study the impact of a change in the type of boundary conditions of an elliptic boundary value problem. In the context of the conductivity equation we consider a reference problem with mixed homogeneous Dirichlet and…
For the $S$ states of two-electron atoms, we introduce an exact and unique factorization of the internal eigenfunction in terms of a marginal amplitude, which depends functionally on the electron-nucleus distances $r_1$ and $r_2$, and a…
A classic no-go theorem in one-dimensional quantum mechanics can be evaded when the potentials are unbounded below, thus allowing for novel parity-paired degenerate energy bound states. We numerically determine the spectrum of one such…
It usually writes the boundary condition of the wave equation in the Coulomb field as a rough form without considering the size of the atomic nucleus. The rough expression brings on that the solutions of the Klein-Gordon equation and the…
The behavior of levels near the threshold of the lower continuum in superheavy H-like atoms with $Z\alpha >1$, caused by the interaction $\Delta U_{AMM}$ of the electron's magnetic anomaly (AMM) dynamically screened at small distances $ \ll…
We consider a uniformly accelerated atom interacting with a vacuum electromagnetic field in the presence of an infinite conducting plane boundary and calculate separately the contributions of vacuum fluctuations and radiation reaction to…
The problem of construction of the Wannier functions (WFs) in a restricted Hilbert space of eigenstates of the one-electron Hamiltonian $\hat{H}$ (forming the so-called low-energy part of the spectrum) can be formulated in several different…
This paper considers to the problems of diffraction of electromagnetic waves on a half-plane, which has a finite inclusion in the form of a Lipschitz curve. The diffraction problem formulated as boundary value problem for Helmholtz…
We re-examine the justification for the imposition of regular boundary conditions on the wavefunction at the Coulomb singularity in the treatment of the hydrogen atom in non-relativistic quantum mechanics. We show that the issue of the…
A model in which a Dirac particle in $\mathbb{R}^{3}$ is bound by $N\geqslant1$ spatially distributed zero-range potentials is presented. Interactions between the particle and the potentials are modeled by subjecting a particle's bispinor…
The purpose of these notes is to provide a pedagogical introduction to the concept of renormalization in atomic physics. We study quantum dynamics of a model of a nonrelativistic single electron atom coupled to the quantum radiation field…
We present a first-principles computational study of solid 4He at T=0K and pressures up to 160GPa. Our computational strategy consists in using van der Waals density functional theory (DFT-vdW) to describe the electronic degrees of freedom…
This paper investigates the asymptotic behavior of a class of nonlinear variational problems with Robin-type boundary conditions on a bounded Lipschitz domain. The energy functional contains a bulk term (the $p$-norm of the gradient), a…
The paper wishes to demonstrate that, in quantum systems with boundaries, different boundary conditions can lead to remarkably different physical behaviour. Our seemingly innocent setting is a one dimensional potential well that is divided…
We study the Dirac-Maxwell system coupled with an external potential of Coulomb type. We use the Foldy--Wouthuysen (unitary) transformation of the Dirac operator and its realization as an elliptic problem in the 4-dim half space…
We reanalyze the problem of a 1D Dirac single particle colliding with the electrostatic potential step of height $V_{0}$ with a positive incoming energy that tends to the limit point of the so-called Klein energy zone, i.e., $E\rightarrow…
In the Randall-Sundrum model where the radion is stabilized by a Goldberger-Wise (GW) potential there is a supercooled transition from a deconfined to a confined phase at temperatures orders of magnitude below the typical Standard Model…