Related papers: Solving for the low-rank tensor components of a sc…
We propose a systematic T-matrix approach to solve few-body problems with s-wave contact interactions in ultracold atomic gases. The problem is generally reduced to a matrix equation expanded by a set of orthogonal molecular states,…
We lift the constraint of a diagonal representation of the Hamiltonian by searching for square integrable bases that support an infinite tridiagonal matrix representation of the wave operator. The class of solutions obtained as such…
We present a new method for the solution of the Schrodinger equation applicable to problems of non-perturbative nature. The method works by identifying three different scales in the problem, which then are treated independently: An…
For a given many-electron molecule, it is possible to define a corresponding one-electron Schr\"odinger equation, using potentials derived from simple atomic densities, whose solution predicts fairly accurate molecular orbitals for single-…
Scattering of charged particles is ubiquitous in nuclear physics. We calculate the proton-proton $s$-wave phase shift at low energy relevant to solar physics. The phase shift is calculated from the ratio of the regular and irregular…
We consider semiclassical Schr\"odinger operators on the real line of the form $$H(\hbar)=-\hbar^2 \frac{d^2}{dx^2}+V(\cdot;\hbar)$$ with $\hbar>0$ small. The potential $V$ is assumed to be smooth, positive and exponentially decaying…
A semi-infinite crack in infinite square lattice is subjected to a wave coming from infinity, thereby leading to its scattering by the crack surfaces. A partially damaged zone ahead of the crack-tip is modeled by an arbitrarily distributed…
In this paper, we consider low-rank approximations for the solutions to the stochastic Helmholtz equation with random coefficients. A Stochastic Galerkin finite element method is used for the discretization of the Helmholtz problem.…
In this paper we present a new highly efficient calculation method for the far field amplitude pattern that arises from scattering problems governed by the d-dimensional Helmholtz equation and, by extension, Schr\"odinger's equation. The…
It was recently observed that chiral two-body interactions can be efficiently represented using matrix factorization techniques such as the singular value decomposition. However, the exploitation of these low-rank structures in a few- or…
An exact method for direct calculation of the Jost functions and Jost solutions for non-central potentials which couple partial waves of different angular momenta is presented. A combination of the variable-constant method with the complex…
A proposal is made for reducing the solution of the N-particle Lippmann-Schwinger equation to that of smaller sets of particles. This consists of first writing the N-particle equation in terms of all possible $N/2$-particle…
We describe the screened Korringa-Kohn-Rostoker (KKR) method and the third-generation linear muffin-tin orbital (LMTO) method for solving the single-particle Schroedinger equation for a MT potential. The simple and popular formalism which…
We establish the existence of positive segregated solutions for competitive nonlinear Schr\"odinger systems in the presence of an external trapping potential, which have the property that each component is obtained from the previous one by…
We represent low dimensional quantum mechanical Hamiltonians by moderately sized finite matrices that reproduce the lowest O(10) boundstate energies and wave functions to machine precision. The method extends also to Hamiltonians that are…
The two-dimensional cubic nonlinear Schr\"{o}dinger equation is used to describe the propagation of an intense laser beam through a medium with Kerr nonlinearity. The coupled two-dimensional cubic nonlinear Schr\"{o}dinger equations are…
We consider an extension of the methodology of the modified method of simplest equation to the case of use of two simplest equations. The extended methodology is applied for obtaining exact solutions of model nonlinear partial differential…
The semiclassically scaled time-dependent multi-particle Schr\"odinger equation describes, inter alia, quantum dynamics of nuclei in a molecule. It poses the combined computational challenges of high oscillations and high dimensions. This…
The reduced-density-matrix method is an promising candidate for the next generation electronic structure calculation method; it is equivalent to solve the Schr\"odinger equation for the ground state. The number of variables is the same as a…
The three-dimensional Schredinger's equation is analyzed with the help of the correspondence principle between classical and quantum-mechanical quantities. Separation is performed after reduction of the original equation to the form of the…