Related papers: Useful Bases for Problems in Nuclear and Particle …

Spectral Barron spaces, constituting a specialized class of function spaces that serve as an interdisciplinary bridge between mathematical analysis, partial differential equations (PDEs), and machine learning, are distinguished by the decay…

A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. We present in a unified and explicit way all these systems of orthogonal polynomials, the associated…

The Bessel function of the first kind $J_{N}\left(kx\right)$ is expanded in a Fourier-Legendre series, as is the modified Bessel functions of the first kind $I_{N}\left(kx\right)$. The purpose of these expansions in Legendre polynomials was…

Assuming Coulomb-like as well as confining scalar potential, we have solved Shr\"odinger equation perturbatively in $1/m_Q$ with a heavy quark mass $m_Q$. The lowest order equation is examined carefully. Mass levels are fitted with…

This paper deals with quon algebras or deformed oscillator algebras, for which the deformation parameter is a root of unity. We show the interest of such algebras for fractional supersymmetric quantum mechanics, angular momentum theory and…

We introduce two-parameter classes of exactly-solvable novel systems whose Hamiltonian operators could be represented by tridiagonal symmetric matrices in some orthogonal bases. The associated wavefunction is written as point-wise…

Quantum and q-deformed algebras find their application not only in mathematical physics and field theoretical context, but also in phenomenology of particle properties. We describe (i) the use of quantum algebras U_q(su_n) corresponding to…

In this paper, by mapping datasets to a set of non-linear coherent states, the process of encoding inputs in quantum states as a non-linear feature map is re-interpreted. As a result of this fact that the Radial Basis Function is recovered…

For a bilinear form obtained by adding a Dirac mass to a positive definite moment functional in several variables, explicit formulas of orthogonal polynomials are derived from the orthogonal polynomials associated with the moment…

Weighted cone-volume functionals are introduced for the convex polytopes in $\mathbb{R}^n$. For these functionals, geometric inequalities are proved and the equality conditions are characterized. A variety of corollaries are derived,…

The q-Laguerre polynomials correspond to an indetermined moment problem. For explicit discrete non-N-extremal measures corresponding to Ramanujan's ${}_1\psi_1$-summation we complement the orthogonal q-Laguerre polynomials into an explicit…

We derive integral representations in terms of the Macdonald functions for the square modulus $s\mapsto | \Gamma ( a + i s ) |^2$ of the Gamma function and its Fourier transform when $a<0$ and $a\not= -1,-2,\ldots $, generalizing known…

A class {\cal R}_p of purely bosonic models is characterized having the following properties in the Bargmann Hilbert space of analytic functions: (i) wave function \psi(\epsilon,z)=\sum_{n=0}^\infty \phi_n(\epsilon) z^n is the {\em…

The framework of Wigner functions for the canonical pair angle and orbital angular momentum, derived and analyzed in 2 recent papers [H. A. Kastrup, Phys.Rev. A 94, 062113(2016) and Phys.Rev. A 95, 052111(2017)] is applied to elementary…

We write spectral decomposition of the hypergeometric differential operator on the contour $Re z=1/2$ (multiplicity of spectrum is 2). As a result, we obtain an integral transform that differs from the Jacobi (or Olevsky) transform. We also…

We derive covariant baryon wave functions for arbitrary Lorentz boosts. Modeling baryons as quark-diquark systems, we reduce their manifestly covariant Bethe-Salpeter equation to a covariant 3-dimensional form by projecting on the relative…

Sets of orthogonal basis functions over two-dimensional circular areas--most often representing pupils in optical applications--are known in the literature for the full circle (Zernike or Jacobi polynomials) and the annulus. This work…

Bochner's theorem gives the necessary and sufficient conditions on a function such that its Fourier transform corresponds to a true probability density function. In the Wigner phase space picture, quantum Bochner's theorem gives the…

Using the theory of orthogonal polynomials, their associated recursion relations and differential formulas we develop a method for evaluating new integrals. The method is illustrated by obtaining a closed-form expression for the value of an…

The quark-meson coupling model, based on a mean field description of non-overlapping nucleon bags bound by the self-consistent exchange of $\sigma$, $\omega$ and $\rho$ mesons, is extended to investigate the properties of finite nuclei.…