Related papers: Solving Many-Electron Schr\"odinger Equation Using…
The neural network method of solving differential equations is used to approximate the electric potential and corresponding electric field in the slit-well microfluidic device. The device's geometry is non-convex, making this a challenging…
Following Ref. [Oriols X 2007 Phys. Rev. Lett., 98 066803], an algorithm to deal with the exchange interaction in non-separable quantum systems is presented. The algorithm can be applied to fermions or bosons and, by construction, it…
Time-dependent wave equations represent an important class of partial differential equations (PDE) for describing wave propagation phenomena, which are often formulated over unbounded domains. Given a compactly supported initial condition,…
We discuss differences and similarities between variational Monte Carlo approaches that use conventional and artificial neural network parameterizations of the ground-state wave function for systems of fermions. We focus on a relatively…
The intertwining operator technique is applied to difference Schroedinger equations with operator-valued coefficients. It is shown that these equations appear naturally when a discrete basis is used for solving a multichannel Schroedinger…
This paper presents analytical solutions for eigenvalues and eigenfunctions of the Schr\"odinger equation in higher dimensions, incorporating the Dunkl operator. Two fundamental quantum mechanical problems are examined in their exact forms:…
We present a theoretical method for calculating multiphoton ionization amplitudes and cross sections of few-electron atoms. The present approach is based on an extraction of partial wave amplitudes from a scattering wave function, which is…
We consider the problem of numerically solving the Schr\"odinger equation with a potential that is quasi periodic in space and time. We introduce a numerical scheme based on a newly developed multi-time scale and averaging technique. We…
A many-body wave function is approximated by a product of two functions: the wave function $\phi$ depending on the particle coordinates and the function $\chi$ depending only on the value of interparticle interaction potential. For the…
We develop several deep learning algorithms for approximating families of parametric PDE solutions. The proposed algorithms approximate solutions together with their gradients, which in the context of mathematical finance means that the…
The integrating factor technique is widely used to solve numerically (in particular) the Schr\"odinger equation in the context of spectral methods. Here, we present an improvement of this method exploiting the freedom provided by the gauge…
The construction of trial wave functions based on neural networks combined with the variational Monte Carlo method is discussed. The mathematical formulation for representing quantum states as artificial neural networks is introduced. The…
Deep neural networks (DNNs) have achieved exceptional performance across various fields by learning complex, nonlinear mappings from large-scale datasets. However, they face challenges such as high memory requirements and computational…
A central problem in quantum mechanics involves solving the Electronic Schrodinger Equation for a molecule or material. The Variational Monte Carlo approach to this problem approximates a particular variational objective via sampling, and…
We take up the idea of Nelson's stochastic processes, the aim of which was to deduce Schr\"odinger's equation. We make two major changes here. The first one is to consider deterministic processes which are pseudo-random but which have the…
We use variable transformation from the real line to finite or semi-infinite spaces where we expand the regular solution of the 1D time-independent Schrodinger equation in terms of square integrable bases. We also require that the basis…
A compression algorithm is introduced for multi-determinant wave functions which can greatly reduce the number of determinants that need to be evaluated in quantum Monte Carlo calculations. We have devised an algorithm with three levels of…
In this work, we study the existence of various classes of standing waves for a nonlinear Schr\"odinger system with quadratic interaction, along with a harmonic or partially harmonic potential. We establish the existence of ground-state…
We study the homogenization of a stochastic Schr\"odinger equation with a large periodic potential in solid state physics. Denoting by $\varepsilon$ the period, the potential is scaled as $\varepsilon^{-2}$. Under a generic assumption on…
We present a novel approach to calculating strong field ionization dynamics of multielectron molecular targets. Adopting a multielectron wavefunction ansatz based on field-free ab initio neutral and ionic multielectron states, a set of…