A matrix representation of the translation operator with respect to a basis set of exponentially declining functions

DOI10.1063/1.524390zbMath0452.33016OpenAlexW2065348639MaRDI QIDQ3898770

E. Otto Steinborn, Eckhard Filter

Publication date: 1980

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.524390

zbMATH Keywords

spherical harmonicexpansions for exponential-type functionsmatrix representation of translation operator

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Spherical harmonics (33C55) Representation theory of linear operators (47A67) (Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces (47A70)

Related Items (16)

Use of Filter-Steinborn \(B\) and Guseinov \({Q_{ns}^q}\) auxiliary functions in evaluation of two-center overlap integrals over Slater type orbitals ⋮ Calculation of three-center nuclear attraction integral over Slater type orbitals in molecular coordinate system using Löwdin \(\alpha \)-radial function and Guseinov's two-center charge density expansion formulae ⋮ AIHFLTF: integrals in Laguerre function bases for electronic structure calculations in atoms ⋮ Calculation of two-center nuclear attraction integrals of Slater type orbitals with noninteger principal quantum numbers using Guseinov's one-center expansion formulas and Löwdin-\(\alpha \) radial function ⋮ On the mathematical nature of Guseinov's rearranged one-range addition theorems for Slater-type functions ⋮ Use of Cartesian coordinates in evaluation of multicenter multielectron integrals over Slater type orbitals and their derivatives ⋮ Unified treatment of complete orthonormal sets for exponential type vector orbitals of particles with spin 1 in coordinate, momentum and four-dimensional spaces ⋮ EVALUATION OF ONE- AND TWO-ELECTRON MULTICENTER INTEGRALS OF YUKAWA-LIKE SCREENED CENTRAL AND NONCENTRAL INTERACTION POTENTIALS OVER SLATER ORBITALS USING ADDITION THEOREMS ⋮ Expansion formulae for two-center integer and noninteger \(n\) STO charge densities and their use in evaluation of multi-center integrals ⋮ Addition theorems for B functions and other exponentially declining functions ⋮ Evaluation of the auxiliary function \(G_{-ns}^{q}\) using basic overlap integrals over Slater type orbitals ⋮ Unified treatment of complete orthonormal sets for wave functions, and Slater orbitals of particles with arbitrary spin in coordinate, momentum and four-dimensional spaces ⋮ Algebraic evaluation of matrix elements in the Laguerre function basis ⋮ Weakly convergent expansions of a plane wave and their use in Fourier integrals ⋮ The Fourier transform of a two-center product of exponential-type functions and its efficient evaluation ⋮ New representations for the spherical tensor gradient and the spherical delta function

Cites Work

• Natural Orbitals in the Quantum Theory of Two-Electron Systems
• On the matrix representation of closed linear operators: An extension of the Von Neumann’s theory
• The three-dimensional convolution of reduced Bessel functions and other functions of physical interest

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