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Related papers: Two-Center Integrals for r_{ij}^{n} Polynomial Cor…

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Schr\"odinger equation for two center Coulomb plus harmonic oscillator potential is solved by the method of ethalon equation at large intercenter separations. Asymptotical expansions for energy term and wave function are obtained in the…

Quantum Physics · Physics 2009-10-31 D. Matrasulov

A new method of solution is proposed for solution of the wave equation in one space dimension with continuously-varying coefficients. By considering all paths along which information arrives at a given point, the solution is expressed as an…

Analysis of PDEs · Mathematics 2019-10-11 Jithin D. George , David I. Ketcheson , Randall J. LeVeque

A class of orthogonal polynomials associated with Coulomb wave functions is introduced. These polynomials play a role analogous to that the Lommel polynomials do in the theory of Bessel functions. The measure of orthogonality for this new…

Classical Analysis and ODEs · Mathematics 2014-04-01 Frantisek Stampach , Pavel Stovicek

The electromagnetic (EM) radiation force-per-length exerted on a pair of electrically-conducting cylindrical particles of circular and non-circular cross-sections is examined using a formal semi-analytical method based on boundary matching…

Classical Physics · Physics 2018-10-09 F. G. Mitri

We obtain certain Mellin-Barnes integrals which present Whittaker wave functions related to classical real split forms of simple complex Lie groups.

Representation Theory · Mathematics 2020-10-30 S. Kharchev , S. Khoroshkin

A method for 3D interpolation between hard spheres is described. The function to be interpolated could be the charge density between atoms in condensed matter. Its electrostatic potential is found analytically, and so are various integrals.…

Materials Science · Physics 2016-09-07 Yoshiro Nohara , O. K. Andersen

The inclusive quasielastic response functions that appear in the scattering of polarized electrons from polarized nuclei are computed and analyzed for several closed-shell-minus-one nuclei with special attention paid to 39K. Results are…

Nuclear Theory · Physics 2008-11-26 J. E. Amaro , J. A. Caballero , T. W. Donnelly , E. Moya de Guerra

A new algorithm to calculate Coulomb wave functions with all of its arguments complex is proposed. For that purpose, standard methods such as continued fractions and power/asymptotic series are combined with direct integrations of the…

Computational Physics · Physics 2009-11-13 N. Michel

Analytical formulas for some useful three-particles integrals are derived. Many of these integrals include Bessel and/or trigonometric functions of one and two interparticle (relative) coordinates $r_{32}, r_{31}$ and $r_{21}$. The formulas…

Mathematical Physics · Physics 2013-12-24 Alexei M. Frolov , David M. Wardlaw

A program for molecular calculations with B functions is reported and its performance is analyzed. All the one- and two-center integrals, and the three-center nuclear attraction integrals are computed by direct procedures, using previously…

Chemical Physics · Physics 2016-02-19 E. O. Steinborn , H. H. H. Homeier , I. Ema , R. Lopez , G. Ramirez

Correlation-function expressions are derived for the coherent nonlinear response of molecules to three resonant ultrafast pulses in the x-ray regime. The ability to create two-core-hole states with controlled attosecond timing in…

Strongly Correlated Electrons · Physics 2009-11-11 Shaul Mukamel

New formulation of relativistic wave equations (RWE) for massive particles with arbitrary half-integer spins s interacting with external electromagnetic fields are proposed. They are based on wave functions which are irreducible tensors of…

High Energy Physics - Theory · Physics 2011-08-17 J. Niederle , A. G. Nikitin

A system of commutative hyperbolic complex numbers in 2 dimensions is studied in this paper. Exponential and trigonometric forms are obtained for these hyperbolic twocomplex numbers. Expressions are given for the elementary functions of…

Complex Variables · Mathematics 2007-05-23 Silviu Olariu

In this work we make some progress on studying four center integrals for the Coulomb energy for both Hartree Fock (HF) and Density Functional Theory (DFT) calculations for small molecules. We consider basis wave functions of the form of an…

Other Condensed Matter · Physics 2024-04-16 Garry Goldstein

An estimation method is presented for polynomial phase signals, i.e., those adopting the form of a complex exponential whose phase is polynomial in its indices. Transcending the scope of existing techniques, the proposed estimator can…

Signal Processing · Electrical Eng. & Systems 2024-11-12 Heedong Do , Namyoon Lee , Angel Lozano

We derive explicit integral formulas for eigenfunctions of quantum integrals of the Calogero-Sutherland-Moser operator with trigonometric interaction potential. In particular, we derive explicit formulas for Jack's symmetric functions. To…

High Energy Physics - Theory · Physics 2009-10-28 Pavel Etingof

The line-dipole approximation for the evaluation of the exciton transfer integral, $J$, between conjugated polymer chains is rigorously justified. Using this approximation, as well as the plane-wave approximation for the exciton…

Chemical Physics · Physics 2007-05-23 William Barford

Resultants are important special functions used in description of non-linear phenomena. Resultant $R_{r_1, ..., r_n}$ defines a condition of solvability for a system of $n$ homogeneous polynomials of degrees $r_1, ..., r_n$ in $n$…

Algebraic Geometry · Mathematics 2008-07-30 A. Morozov , Sh. Shakirov

We present a wavefunction-based approach to correlated ab initio calculations on crystalline insulators of infinite extent. It uses the representation of the occupied and the unoccupied (virtual) single-particle states of the infinite solid…

Condensed Matter · Physics 2009-10-31 Alok Shukla , Michael Dolg , Peter Fulde , Hermann Stoll

The energy and wave function of a harmonically confined two-electron system coupled to light is calculated by separating the wave functions of the relative and center of mass (CM) motions. The relative motion wave function has a known…

Mesoscale and Nanoscale Physics · Physics 2021-11-10 Chenhang Huang , Alexander Ahrens , Matthew Beutel , Kalman Varga