Related papers: Theory and Computation of the Spheroidal Wave Func…
The problem of scattering of harmonic plane acoustic waves by fluid spheroids (prolate and oblate) is addressed from an analytical approach. Mathematically, it consists in solving the Helmholtz equation in an unbounded domain with…
The perturbation method in supersymmetric quantum mechanics (SUSYQM) is used to study the spheroidal wave functions' eigenvalue problem. Expanding the super-potential in series of the parameter alpha, the first order term of ground…
The Heun function generalizes all well-known special functions such as Spheroidal Wave, Lame, Mathieu, and hypergeometric_2F_1,_1F_1 and_0F_1 functions. Heun functions are applicable to diverse areas such as theory of black holes, lattice…
A computation scheme for solving elliptic boundary value problems with axially symmetric confining potentials using different sets of one-parameter basis functions is presented. The efficiency of the proposed symbolic-numerical algorithms…
Since 1908, when Mie reported analytical expressions for the fields scattered by a spherical particle upon incidence of an electromagnetic plane-wave, generalizing his analysis to the case of an arbitrary incident wave has proved elusive.…
Analytical solutions to acoustic scattering problems involving nonspherical shapes, such as spheroids and disks, have long been known and have many applications. However, these solutions require special functions that are not easily…
We present a unified approach for constructing Slepian functions - also known as prolate spheroidal wave functions - on the sphere for arbitrary tensor ranks including scalar, vectorial, and rank 2 tensorial Slepian functions, using…
The aim of this work is to define a continuous functional calculus in quaternionic Hilbert spaces, starting from basic issues regarding the notion of spherical spectrum of a normal operator. As properties of the spherical spectrum suggest,…
Exploring strongly correlated spinful states of few fermionic ultracold atoms in a rapidly rotating trap, an example of which was recently realized for two fermionic $^6$Li atoms in an optical tweezer, we derive analytical (algebraic)…
The analytical expression for angular integral flux of atmospheric muons in matter with the explicit relation of its parameters with those of the sea level spectrum is obtained. The fitting formula for the sea level muon spectrum at…
This chapter introduces the main ideas and the most important methods for representing the electronic wavefunction through machine learning models. The wavefunction of a N-electron system is an incredibly complicated mathematical object,…
We review some aspects of the theory of spherical Bessel functions and Struve functions by means of an operational procedure essentially of umbral nature, capable of providing the straightforward evaluation of their definite integrals and…
In this paper we aim to give various explicit and local estimates of ball prolate spheroidal wave functions defined in [25] as eigenfunctions of both finite Fourier transform and some differential operator. In particular, we give further…
It is shown that evolution of an open quantum system can be exactly described in terms of wave function which obeys Schrodinger equation with randomly varying parameters whose statistics is universally determined by separate dynamics of the…
We introduce a systematically improvable family of variational wave functions for the simulation of strongly correlated fermionic systems. This family consists of Slater determinants in an augmented Hilbert space involving "hidden"…
The classical solution to the Helmholtz wave equation in spherical coordinates is well known and has found many important applications in wave propagation, scattering, and imaging in optics and acoustics. The separable solution is comprised…
We present an efficient multi-accuracy algorithm for the computations of a set of special functions of a complex argument, z=x+iy. These functions include the complex probability function w(z), and closely related functions such as the…
We present series study of using the method of super-symmetric quantum mechanics(SUSYQM) solving the spin-weighted spheroidal wave equation. In this paper, we obtain the first four terms of super-potential of the spin-weighted spheroidal…
Within the framework of probability distributions on projective Hilbert space a scheme for the calculation of multitime correlation functions is developed. The starting point is the Markovian stochastic wave function description of an open…
The authors present SHarmonic, a new implementation of the spherical harmonics targeted for electronic-structure calculations. Their approach is to use explicit formulas for the harmonics written in terms of normalized Cartesian…