Related papers: Sharp regularity results for many-electron wave fu…
We present an exact decomposition of the complete wavefunction for a system of nuclei and electrons evolving in a time-dependent external potential. We derive formally exact equations for the nuclear and electronic wavefunctions that lead…
Quantum mechanical scalar particle with polarizability is considered in the presence of the Coulomb field. Separation of variables is performed with the use of Wigner $D$-functions, the radial system of 15 equations is reduced to a single…
Two-direction multiscaling functions $\boldsymbol{\phi}$ and two-direction multiwavelets $\boldsymbol{\psi}$ associated with $\boldsymbol{\phi}$ are more general and more flexible setting than one-direction multiscaling functions and…
In this paper we develop the notion of ergodicity to include functions dominated by a weight $w$. Such functions have polynomial means and include, amongst many others, the $w$-almost periodic functions. This enables us to describe the…
Modulated electroreflectance spectroscopy $\Delta R/R$ of semiconductor self-assembled quantum dots is investigated. The structure is modeled as dots with lens shape geometry and circular cross section. A microscopic description of the…
The asymptotic behavior in the leading order of the continuous spectrum eigenfunctions $\Psi(\bz,\bq)$ as $|\bz|\rightarrow\infty$ for the system of three three-dimensional charged quantum particles has been obtained on the heuristic level.…
We consider the Hartree equation for infinitely many electrons with a constant external magnetic field. For the system, we show a local well-posedness result when the initial data is the pertubation of a Fermi sea, which is a non-trace…
In this contribution we study the accuracy of various forms of electron effective mass equation in reproducing spectral and spin-related features of quantum dot systems. We compare the results of the standard 8 band k.p model to those…
For parameter identification problems the Fr\'echet-derivative of the parameter-to-state map is of particular interest. In many applications, e.g. in seismic tomography, the unknown quantity is modeled as a coefficient in a linear…
We consider high order approximations of the solution of the stochastic filtering problem, derive their pathwise representation in the spirit of the earlier work of Clark and Davis and prove their robustness property. In particular, we show…
An experiment is presented in which the alleged progression of a photon's wave function is ``measured'' by a row of superposed atoms. The photon's wave function affects only one out of the atoms, regardless of its position within the row,…
Schr{\"o}dinger noticed in 1952 that a scalar complex wave function can be made real by a gauge transformation. The author showed recently that one real function is also enough to describe matter in the Dirac equation in an arbitrary…
Given a redundant dictionary $\Phi$, represented by an $M \times N$ matrix ($\Phi \in \mathbb{R}^{M \times N}$) and a target signal $y \in \mathbb{R}^M$, the \emph{sparse approximation problem} asks to find an approximate representation of…
In this study, we have performed a detailed investigation of the electronic properties of a core/shell/well/shell multi-layered spherical quantum dot, such as energy eigenvalues, wave functions, electron probability distribution and binding…
Spherical Harmonics, $Y_\ell^m(\theta,\phi)$, are derived and presented (in a Table) for half-odd-integer values of $\ell$ and $m$. These functions are eigenfunctions of $L^2$ and $L_z$ written as differential operators in the…
We study two irrationality measure functions $\psi_\alpha^{[2]} (t) $ and $\psi_\alpha^{[2]*} (t)$ related to the "second best" approximations to a real numbers and prove some results on the structure of the corresponding Diophantine…
We consider several formalizations in the language of second-order arithmetic of "The formula $\phi$ is a theorem of $\omega$-logic", including some which have been studied in the literature and a new variant defined via a least fixed…
In heavy atoms and molecules, on the distances $a \gg Z^{-1}$ from all of the nuclei (with a charge $Z_m$) we prove that $\rho_\Psi (x)$ is approximated in $L^p$-norm, by the Thomas-Fermi density.
Within the Schroedinger Electric Representation we analytically calculate the complete wave functional obeying Gauss' law with static SU(2) sources in (1+1)-dimensions. The effective potential is found to be linear in the distance between…
Consider the wave equation associated with the Kohn Laplacian on groups of Heisenberg type. We construct parametrices using oscillatory integral representations and use them to prove sharp $L^p$ and Hardy space regularity results.