Related papers: Sharp regularity results for many-electron wave fu…
Stationary-state Schr{\"o}dinger-Pauli theory is a description of electrons with a spin moment in an external electromagnetic field. For 2-electron systems as described by the Schr{\"o}dinger-Pauli theory Hamiltonian with a symmetrical…
Asymptotic representations for large values of the hyperradius are constructed for the scattering wave function of a system of $ N $ particles considered as a generalized function of angular variable coordinates. The coefficients of the…
The subject of this work is the analysis of hadronic decays of the exotic meson $\pi_{1}$ in a fully relativistic formalism, and comparison with the nonrelativistic results. The relativistic spin wave functions of mesons and hybrids are…
We argue that the double-slit experiment can be understood much better by considering it as an experiment whereby one uses electrons to study the set-up rather than an experiment whereby we use a set-up to study the behaviour of electrons.…
The paper discusses relations between the structure of the complex Fermi surface below the spectrum of a second order periodic elliptic equation and integral representations of certain classes of its solutions. These integral…
Transformation of the conventional radial Schr\"odinger equation defined on the interval $\,r\in[0,\infty)$ into an equivalent form defined on the finite domain $\,y(r)\in [a,b]\,$ allows the s-wave scattering length $a_s$ to be exactly…
Given an automaton (a letter-to-letter transducer, a dynamical 1-Lipschitz system on the space $\mathbb Z_p$ of $p$-adic integers) $\mathfrak A$ whose input and output alphabets are $\mathbb F_p=\{0,1,\ldots,p-1\}$, one visualizes word…
We provide analytic solutions of the nonlinear differential equation system describing the particle paths below small-amplitude periodic gravity waves travelling on a constant vorticity current. We show that these paths are not closed…
We investigate the symmetry properties for Baym's $\Phi$-derivable schemes. We show that in general the solutions of the dynamical equations of motion, derived from approximations of the $\Phi$-functional, do not fulfill the Ward-Takahashi…
We find a uniform semiclassical (SC) wave function describing coherent branched flow through a two-dimensional electron gas (2DEG), a phenomenon recently discovered by direct imaging of the current using scanned probed microscopy. The…
Spherical representations and functions are the building blocks for harmonic analysis on riemannian symmetric spaces. In this paper we consider spherical functions and spherical representations related to certain infinite dimensional…
In this paper, we study the performance of Full Waveform Inversion (FWI) from time-harmonic Cauchy data via conditional well-posedness driven iterative regularization. The Cauchy data can be obtained with dual sensors measuring the pressure…
We consider elliptic second order partial differential operators with Lipschitz continuous leading order coefficients on finite cubes and the whole Euclidean space. We prove quantitative sampling and equidistribution theorems for…
We present a new efficient numerical approach for representing anisotropic physical quantities and/or matrix elements defined on the Fermi surface of metallic materials. The method introduces a set of numerically calculated generalized…
The equation is considered for a composite scalar particle with polarizabilities in an external quantized electromagnetic plane wave. This equation is reduced to a system of equations for infinite number of interacting oscillators. After…
We report an infinite number of orthonormal wave functions bases for the quantum problem of a free particle in presence of an applied external magnetic field. Each set of orthonormal wave functions (basis) is labeled by an integer $p$,…
Schr{\"o}dinger-Pauli (SP) theory is a description of electrons in the presence of a static electromagnetic field in which the interaction of the magnetic field with both the orbital and spin moments is explicitly considered. The theory is…
The aim of this paper is to find an expression for second derivative of the function $\phi(t)$ defined by $$\phi(t) = \lt(\int_V \vphi(t,x)^{-\beta} dx\rt)^{-\frac1{\be -n}},\qquad \beta\not= n,$$ where $U\subset \R$ and $V\subset \R^n$ are…
We get a local existence result in $H^s$ with $s>3/2$ for second order quasilinear wave equation with radial initial data in 2+1 dimensions, based on an improvement of Strichartz estimate in the radial case. Moreover, we get the…
Harmonic wave functions for integer and half-integer angular momentum are given in terms of the Euler angles $(\theta,\phi,\psi)$ that define a rotation in $SO(3)$, and the Euclidean norm in ${\mathbb R}^3$. Following a classical work by…