Related papers: Using a computer algebra system to simplify expres…
The Wigner-Weyl isomorphism for quantum mechanics on a compact simple Lie group $G$ is developed in detail. Several New features are shown to arise which have no counterparts in the familiar Cartesian case. Notable among these is the notion…
We show that sampling or interpolation formulas in reproducing kernel Hilbert spaces can be obtained by reproducing kernels whose dual systems form molecules, ensuring that the size profile of a function is fully reflected by the size…
We present a small computer algebra program for use in Maxwell's theory. The Maxwell equations and the energy-momentum current of the electromagnetic field are formulated in the language of exterior differential forms. The corresponding…
A double-atom partitioning of the molecular one-electron density matrix is used to describe atoms and bonds. All calculations are performed in Hilbert space. The concept of atomic weight functions (familiar from Hirshfeld analysis of the…
We consider a generalization of polynomial programs: algebraic programs, which are optimization or feasibility problems with algebraic objectives or constraints. Algebraic functions are defined as zeros of multivariate polynomials. They are…
A new and computationally viable full quantum version of line shape theory is obtained in terms of a mixed Weyl symbol calculus. The basic ingredient in the collision--broadened line shape theory is the time dependent dipole autocorrelation…
The purpose of this note is to survey a methodology to solve systems of polynomial equations and inequalities. The techniques we discuss use the algebra of multivariate polynomials with coefficients over a field to create large-scale linear…
We present a package to perform partial fraction decompositions of multivariate rational functions. The algorithm allows to systematically avoid spurious denominator factors and is capable of producing unique results also when being applied…
Computer algebra is widely used in various fields of mathematics, physics and other sciences. The simplification of tensor expressions is an important special case of computer algebra. In this paper, we consider the reduction of tensor…
We introduce variational methods for finding approximate eigenfunctions and eigenvalues of quantum Hamiltonians by constructing a set of orthogonal wave functions which approximately solve the eigenvalue equation.
In this work we present the computer algebra package HarmonicSums and its theoretical background for the manipulation of harmonic sums and some related quantities as for example Euler-Zagier sums and harmonic polylogarithms. Harmonic sums…
In this article we present a method to implement orthogonal polynomials and many other special functions in Computer Algebra systems enabling the user to work with those functions appropriately, and in particular to verify different types…
We illustrate the main features of a recently proposed method based on ensemble density functional theory to divide rigorously a complex molecular system into its parts [M.H. Cohen and A. Wasserman, J. Phys. Chem. A 111, 2229 (2007)]. The…
We present a phase-space representation of the hydrogen atom using the Kirkwood-Rikaczek distribution function. This distribution allows us to obtain analytical results, which is quite unique because an exact analytical form of the Wigner…
Regular chains and triangular decompositions are fundamental and well-developed tools for describing the complex solutions of polynomial systems. This paper proposes adaptations of these tools focusing on solutions of the real analogue:…
Quantum Mechanics and Signal Processing in the line R, are strictly related to Fourier Transform and Weyl-Heisenberg algebra. We discuss here the addition of a new discrete variable that measures the degree of the Hermite functions and…
We construct the integral transform passing from the space representation to the momentum representation for the Hydrogen atom using polar spherical coordinates. The resulting radial wave functions are explicitly given in terms of complex…
In this paper we present an algorithmic procedure that transforms, if possible, a given system of ordinary or partial differential equations with radical dependencies in the unknown function and its derivatives into a system with polynomial…
With the exception of q-hypergeometric summation, the use of computer algebra packages implementing Zeilberger's "holonomic systems approach" in a broader mathematical sense is less common in the field of q-series and basic hypergeometric…
The main difficulty in utilizing the O(4) symmetry of the Hydrogen atom in practical calculations is the dependence of the Fock stereographic projection on energy. This is due to the fact that the wave functions of the states with different…