Related papers: Solving Many-Electron Schr\"odinger Equation Using…
An O(N) algorithm is proposed for calculating linear response functions of non-interacting electrons in arbitray potential. This algorithm is based on numerical solution of the time-dependent Schroedinger equation discretized in space, and…
We use a variational Monte Carlo algorithm to solve the electronic structure of two-dimensional semiconductor quantum dots in external magnetic field. We present accurate many-body wave functions for the system in various magnetic field…
The Schr\"odinger equation relates the electron wavefunction and the electric potential, which are emergent physical quantities. At that emergent level, the Schr\"odinger equation is either postulated as a principle of quantum physics or…
The ground-breaking works of Weinberg have opened the way to calculations of atomic nuclei that are based on systematically improvable Hamiltonians. Solving the associated many-body Schr\"odinger equation involves non-trivial difficulties,…
We propose a bilinear sampling algorithm in Green's function Monte Carlo for expectation values of operators that do not commute with the Hamiltonian and for differences between eigenvalues of different Hamiltonians. The integral…
The hybridizations of machine learning and quantum physics have caused essential impacts to the methodology in both fields. Inspired by quantum potential neural network, we here propose to solve the potential in the Schrodinger equation…
The configuration interaction approach provides a conceptually simple and powerful approach to solve the Schr\"odinger equation for realistic molecules and materials but is characterized by an unfavourable scaling, which strongly limits its…
We show that a nonlinear Schr\"odinger wave equation can reproduce all the features of linear quantum mechanics. This nonlinear wave equation is obtained by exploring, in a uniform language, the transition from fully classical theory…
Diffusion Monte Carlo (DMC) based on fixed-node approximation has enjoyed significant developments in the past decades and become one of the go-to methods when accurate ground state energy of molecules and materials is needed. The remaining…
Fractional evolution equations lack generally accessible and well-converged codes excepting anomalous diffusion. A particular equation of strong interest to the growing intersection of applied mathematics and quantum information science and…
Machine learning and specifically deep-learning methods have outperformed human capabilities in many pattern recognition and data processing problems, in game playing, and now also play an increasingly important role in scientific…
The semiclassical Schr\"{o}dinger equation with multiscale and random potentials often appears when studying electron dynamics in heterogeneous quantum systems. As time evolves, the wavefunction develops high-frequency oscillations in both…
In this paper we suggest a new approach for the multichannel Coulomb scattering problem. The Schr\"{o}dinger equation for the problem is reformulated in the form of a set of inhomogeneous equations with a finite-range driving term. The…
By decomposing the important sampled imaginary time Schr\"odinger evolution operator to fourth order with positive coefficients, we derived a number of distinct fourth order Diffusion Monte Carlo algorithms. These sophisticated algorithms…
We propose a numerical method for evaluating eigenvalues and eigenfunctions of Schr\"odinger operators with general confining potentials. The method is selective in the sense that only the eigenvalue closest to a chosen input energy is…
We develop a new method for solving two- and three-body bound state problems using unsupervised machine learning techniques. We use a deep neural network to calculate both simple and realistic potentials, obtaining the properties of the…
A modified algorithm is proposed to include Pauli exclusion principle in Monte-Carlo simulations. This algorithm has significant advantages to implement in terms of simplicity, speed and memory storage. We show that even in moderately high…
The Schrodinger equation is one of the most important equations in physics and chemistry and can be solved in the simplest cases by computer numerical methods. Since the beginning of the 70s of the last century the computer began to be used…
Solutions of time-independent Schrodinger equation for potentials periodic in space satisfy Bloch theorem. The theorem has been used to obtain solutions of the Schrodinger equation for periodic systems by expanding them in terms of plane…
Multi-dimensional direct numerical simulation (DNS) of the Schr\"odinger equation is needed for design and analysis of quantum nanostructures that offer numerous applications in biology, medicine, materials, electronic/photonic devices,…