Related papers: Matrix elements of the Argonne v18 potential

Matrix elements between shifted correlated Gaussians of various potentials with several form-factors are calculated analytically. Analytic matrix elements are of importance for the correlated Gaussian method in quantum few-body physics.

This article describes a method for calculating S-matrix elements using Hamiltonians obtained in the renormalization group procedure for effective particles. It is shown that the scattering amplitudes obtained using a canonical Hamiltonian…

We briefly review our works for graviton and spherical graviton potentials in a plane-wave matrix model. To compute them, it is necessary to devise a configuration of the graviton solutions, since the plane-wave matrix model includes mass…

The problem of evaluating potential integrals on planar triangular elements has been addressed using a polar coordinate decomposition. The resulting formulae are general, exact, easily implemented, and have only one special case, that of a…

A variational and perturbative treatment is provided for a family of generalized spiked harmonic oscillator Hamiltonians H = -(d/dx)^2 + B x^2 + A/x^2 + lambda/x^alpha, where B > 0, A >= 0, and alpha and lambda denote two real positive…

In this paper we derive expressions for matrix elements (\phi_i,H\phi_j) for the Hamiltonian H=-\Delta+\sum_q a(q)r^q in d > 1 dimensions. The basis functions in each angular momentum subspace are of the form…

The two-electron problem for the helium-like atom/ions in $S$-state is considered. The basis containing the integer powers of $\ln r$, where $r$ is a radial variable of the Fock expansion, is studied. In this basis, the analytic expressions…

The inverse of an $\infty \times \infty$ symmetric band matrix can be constructed in terms of a matrix continued fraction. For Hamiltonians with Coulomb plus polynomial potentials, this results in an exact and analytic Green's operator…

Precision tests of the Standard Model and searches for beyond the Standard Model physics often require nuclear structure input. There has been a tremendous progress in the development of nuclear ab initio techniques capable of providing…

Within the framework of the quark model and the variational method, the bound states of four heavy quarks (tetraquarks) are investigated. The basis variational wave functions are chosen in the Gaussian form. The matrix elements of the…

It is considered that the effective interaction between any two quarks in a baryon can be approximately described by a simple harmonic potential. Also, it is made use of the nonrelativistic approximation. The problem is firstly solved in…

We present a new approach for the Talmi-Moshinsky transformation representation in the harmonic oscillator basis. We utilize the SU(3) scheme for the calculation of harmonic oscillator brackets. Using this scheme we obtain the explicit…

Matrix elements of potential energy are examined in detail. We consider a model problem - a particle in a central potential. The most popular forms of central potential are taken up, namely, square-well potential, Gaussian, Yukawa and…

Using a complete basis set we have obtained an analytic expression for the matrix elements of the Coulomb interaction. These matrix elements are written in a closed form. We have used the basis set of the three-dimensional isotropic quantum…

The finite-element approach to lattice field theory is both highly accurate (relative errors $\sim 1/N^2$, where $N$ is the number of lattice points) and exactly unitary (in the sense that canonical commutation relations are exactly…

Motivated by recently developed techniques making it possible to compute Casimir energies for any object whose scattering S-matrix (or, equivalently, T-matrix) is available, we develop a variable phase method to compute the S-matrix for…

Electronic structure methods that exploit nonorthogonal Slater determinants face the challenge of efficiently computing nonorthogonal matrix elements. In a recent publication, H. G. A. Burton, J. Chem. Phys. 154, 144109 (2021), I introduced…

The problem of the harmonic oscillator with a centrally located delta function potential can be exactly solved in one dimension where the eigenfunctions are expressed as superpositions of the Hermite polynomials or as confluent…

Atomic effective one-electron potentials in a compact analytic form in terms of a few Gaussian charge distributions are developed, for Hydrogen through Nobelium, for starting molecular electronic structure calculations by a simple…

This paper describes a method of calculating the transforms, currently obtained via Fourier and reverse Fourier transforms. The method allows calculating efficiently the transforms of a signal having an arbitrary dimension of the digital…