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Atomic and molecular breakup reactions, such as multiple-ionisation, are described by a driven Schr\"odinger equation. This equation is equivalent to a high-dimensional Helmholtz equation and it has solutions that are outgoing waves,…

Numerical Analysis · Mathematics 2022-03-22 Jacob Snoeijer , Wim Vanroose

The electronic Schr\"odinger equation describes the motion of $N$ electrons under Coulomb interaction forces in a field of clamped nuclei. It is proved that its solutions for eigenvalues below the essential spectrum lie in the spectral…

Analysis of PDEs · Mathematics 2026-04-10 Harry Yserentant

The emergence of machine learning methods in quantum chemistry provides new methods to revisit an old problem: Can the predictive accuracy of electronic structure calculations be decoupled from their numerical bottlenecks? Previous attempts…

Computational Physics · Physics 2020-08-26 M. Gastegger , A. McSloy , M. Luya , K. T. Schütt , R. J. Maurer

Inspired by the universal approximation theorem and widespread adoption of artificial neural network techniques in a diversity of fields, we propose feed-forward neural networks as a general purpose trial wave function for quantum Monte…

Computational Physics · Physics 2021-01-26 Jan Kessler , Francesco Calcavecchia , Thomas D. Kühne

In this paper we present a novel multiscale splitting approach to solve multiscale Schroedinger equation, which have large different time-scales. The energy potential is based on highly oscillating functions, which are magnitudes faster…

Numerical Analysis · Mathematics 2018-05-31 Juergen Geiser , Amirbahador Nasari

Shor's factoring algorithm illustrates the potential power of quantum computation. Here we present and numerically investigate a proposal for a compiled version of such an algorithm based on a quantum-wire network exploiting the…

Quantum Physics · Physics 2011-01-14 Fabrizio Buscemi

The nonlinear Schrodinger equation is a classical integrable equation which contains plenty of significant properties and occurs in many physical areas. However, due to the difficulty of solving this equation, in particular in high…

Exactly Solvable and Integrable Systems · Physics 2020-11-20 Juncai Pu , Jun Li , Yong Chen

Fully numerical mesh solutions of 2D and 3D quantum equations of Schroedinger and Hartree-Fock type allow us to work with wavefunctions which possess a very flexible geometry. This flexibility is especially important for calculations of…

Atomic Physics · Physics 2007-05-23 Mikhail V. Ivanov

Physics-informed neural networks (PINN) have been widely used in computational physics to solve partial differential equations (PDEs). In this study, we propose an energy-embedding-based physics-informed neural network method for solving…

Computational Physics · Physics 2025-06-02 Yi-Qiang Wu , Xuan Liu , Hanlin Li , Fuqiang Wang

In this paper we study quantum simulation algorithms on the elastic wave equations using the Schr\"odingerisation method. The Schr\"odingerisation method transforms any linear PDEs into a system of Schr\"odinger-type PDEs -with unitary…

Quantum Physics · Physics 2025-05-27 Shi Jin , Chundan Zhang

We propose a novel wave function partitioning method that integrates deep-learning variational Monte Carlo with ans\"atze based on generalized product functions. This approach effectively separates electronic wave functions (WFs) into…

Chemical Physics · Physics 2025-06-24 Matěj Mezera , Paolo A. Erdman , Zeno Schätzle , P. Bernát Szabó , Frank Noé

We present a multidimensional deep learning implementation of a stochastic branching algorithm for the numerical solution of fully nonlinear PDEs. This approach is designed to tackle functional nonlinearities involving gradient terms of any…

Numerical Analysis · Mathematics 2023-09-12 Jiang Yu Nguwi , Guillaume Penent , Nicolas Privault

We use a diffusion Monte Carlo method to solve the many-body Schr\"odinger equation describing fully-heavy tetraquark systems. This approach allows to reduce the uncertainty of the numerical calculation at the percent level, accounts for…

High Energy Physics - Phenomenology · Physics 2020-12-30 M. C. Gordillo , F. De Soto , J. Segovia

We demonstrate that it is possible to compute wave function normalization constants for a class of Schr\"odinger type equations by an algorithm which scales linearly (in the number of eigenfunction evaluations) with the desired precision P…

Mathematical Physics · Physics 2011-05-10 Amna Noreen , Kåre Olaussen

Artificial neural networks have been successfully incorporated into variational Monte Carlo method (VMC) to study quantum many-body systems. However, there have been few systematic studies of exploring quantum many-body physics using deep…

Strongly Correlated Electrons · Physics 2020-02-26 Li Yang , Zhaoqi Leng , Guangyuan Yu , Ankit Patel , Wen-Jun Hu , Han Pu

Machine learning techniques have proven to be effective in addressing the structure of atomic nuclei. Physics$-$Informed Neural Networks (PINNs) are a promising machine learning technique suitable for solving integro-differential problems…

Computational Physics · Physics 2026-02-13 Lorenzo Brevi , Antonio Mandarino , Carlo Barbieri , Enrico Prati

Multi-time wave functions are wave functions that have a time variable for every particle, such as $\phi(t_1,x_1,\ldots,t_N,x_N)$. They arise as a relativistic analog of the wave functions of quantum mechanics but can be applied also in…

Quantum Physics · Physics 2014-03-28 Sören Petrat , Roderich Tumulka

In this paper, the classical Schr\"odinger equation, which allows the study of classical dynamics in terms of wave functions, is analyzed theoretically and numerically. First, departing from classical (Newtonian) mechanics, and assuming an…

Quantum Physics · Physics 2016-11-23 Albert Benseny , David Tena , Xavier Oriols

Finding accurate solutions to the electronic Schr\"odinger equation plays an important role in discovering important molecular and material energies and characteristics. Consequently, solving systems with large numbers of electrons has…

Machine Learning · Computer Science 2024-01-22 Shai Pranesh , Shang Zhu , Venkat Viswanathan , Bharath Ramsundar

The Darwin-Howie-Whelan equations are commonly used to describe and simulate the scattering of fast electrons in transmission electron microscopy. They are a system of infinitely many envelope functions, derived from the Schr\"odinger…

Mathematical Physics · Physics 2022-04-21 Thomas Koprucki , Anieza Maltsi , Alexander Mielke