Weakly convergent expansions of a plane wave and their use in Fourier integrals
From MaRDI portal
Publication:3678162
DOI10.1063/1.526970zbMath0564.43009OpenAlexW2019235368MaRDI QIDQ3678162
Publication date: 1985
Published in: Journal of Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1063/1.526970
Fourier transformplane wavespherical harmonicsspherical tensorspherical Bessel functionsRayleigh expansion
Integral transforms in distribution spaces (46F12) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Harmonic analysis and spherical functions (43A90)
Related Items (16)
On the evaluation of integrals with Coulomb Sturmian radial functions ⋮ A bi-directional method for evaluating integrals involving higher transcendental functions. HyperRAF: a Julia package for new hyper-radial functions ⋮ On the mathematical nature of Guseinov's rearranged one-range addition theorems for Slater-type functions ⋮ The genesis and early developments of Aitken's process, Shanks' transformation, the \(\varepsilon\)-algorithm, and related fixed point methods ⋮ 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 ⋮ Addition theorems for B functions and other exponentially declining functions ⋮ Bessel, sine and cosine functions and extrapolation methods for computing molecular multi-center integrals ⋮ Unified treatment of complete orthonormal sets of nonrelativistic, quasirelativistic and relativistic sets of spinor wave functions, and Slater spinor orbitals in coordinate, momentum and four-dimensional spaces ⋮ Unified treatment of complete orthonormal sets for wave functions, and Slater orbitals of particles with arbitrary spin in coordinate, momentum and four-dimensional spaces ⋮ Variational Sturmian approximation: A nonperturbative method of solving time-independent Schrödinger equation ⋮ The Fourier transform method and the \(S\overline D\) approach for the analytical and numerical treatment of multicenter overlap-like quantum similarity integrals ⋮ Convergence of translation formulas for the computation of multicenter integrals over Slater orbitals ⋮ Algebraic evaluation of matrix elements in the Laguerre function basis ⋮ Harmonic polynomials, hyperspherical harmonics, and atomic spectra ⋮ Relativistic bound-state calculations in light-front dynamics
Uses Software
Cites Work
- Quadrature formulas for oscillatory integral transforms
- Natural Orbitals in the Quantum Theory of Two-Electron Systems
- Wigner Coefficients for the R4 Group and Some Applications
- New representations for the spherical tensor gradient and the spherical delta function
- A matrix representation of the translation operator with respect to a basis set of exponentially declining functions
- Numerical evaluation of integrals containing a spherical Bessel function by product integration
- Notes on O(4) Representations
This page was built for publication: Weakly convergent expansions of a plane wave and their use in Fourier integrals