Related papers: Theory and Computation of the Spheroidal Wave Func…
The integral of the Wigner function of a quantum mechanical system over a region or its boundary in the classical phase plane, is called a quasiprobability integral. Unlike a true probability integral, its value may lie outside the interval…
One of the fundamental problems in communications is finding the energy distribution of signals in time and frequency domains. It should, therefore, be of great interest to find the most energy concentration hypercomplex signal. The present…
Experiments using intermediate- to high-energy radioactive nuclear beams present numerous findings. Extracting important properties of physical observables relies on a firm theoretical analysis. Though Glauber theory is believed to work…
The dynamic interactions between pairs of swimming microorganisms underpin the collective behaviour of larger suspensions, but accurately calculating pairwise collisions has typically required the use of numerical simulations in which…
Single-particle resonance parameters and wave functions in spherical and deformed nuclei are determined through analytic continuation in the potential strength. In this method, the analyticity of the eigenvalues and eigenfunctions of the…
Within the well-established optical response function formalism, a new strategy with the central idea of employing the forward-backward stochastic Schr\"{o}dinger equations in a segmented way to accurately obtain the two-dimensional (2D)…
Representing fermionic wavefunctions efficiently is a central problem in quantum physics, chemistry and materials science. In this work, we introduce a universal and exact representation of continuous antisymmetric functions by lifting them…
Standard power series are used to construct and analyze angular and radial spheroidal functions, which are necessary for solving boundary value problems for Helmholtz equation in a spheroid. With an advanced approach the low-lying energy…
We extend some definitions and give new results about the theory of slice analysis in several quaternionic variables. The sets of slice functions which are respectively slice, slice regular and circular w.r.t. given variables are…
A consistent functional calculus approach to the spectral theorem for strongly commuting normal operators on Hilbert spaces is presented. In contrast to the common approaches using projection-valued measures or multiplication operators,…
The spectral theory on the $S$-spectrum was born out of the need to give quaternionic quantum mechanics (formulated by Birkhoff and von Neumann) a precise mathematical foundation. Then it turned out that this theory has important…
A collection of algorithms in object-oriented MATLAB is described for numerically computing with smooth functions defined on the unit ball in the Chebfun software. Functions are numerically and adaptively resolved to essentially machine…
We prove mixed-norm estimates for circular averages with respect to $\alpha$-dimensional fractal measures on $\mathbb{R}^2$, using circle tangency bounds when $\alpha \in (0,1]$ and a $\delta$-discretized slicing lemma for fractals when…
The numerical treatment of quantum mechanics in the semi-classical regime is known to be computationally demanding, due to the highly oscillatory behaviour of the wave function and its large spatial extension. A recently proposed…
We argue that quaternions form a natural language for the description of quantum-mechanical wavefunctions with spin. We use the quaternionic spinor formalism which is in one-to-one correspondence with the usual spinor language. No…
Computing spherical harmonic decompositions is a ubiquitous technique that arises in a wide variety of disciplines and a large number of scientific codes. Because spherical harmonics are defined by integrals over spheres, however, one must…
Mathematical justifications are given for several integral and series representations of the Dirac delta function which appear in the physics literature. These include integrals of products of Airy functions, and of Coulomb wave functions;…
A matrix basis formulation is introduced to represent the 3 x 3 dyadic Green's functions in the frequency domain for the Maxwell's equations and the elastic wave equation in layered media. The formulation can be used to decompose the…
In this paper, we introduce the prolate spheroidal wave functions (PSWFs) of real order $\alpha>-1$ on the unit ball in arbitrary dimension, termed as ball PSWFs. They are eigenfunctions of both a weighted concentration integral operator,…
This paper is a tutorial that demonstrates various methods from the Colombeau theory of generalized functions in the context of semilinear wave equations. The Colombeau generalized functions constitute differential algebras that contain the…