Machine learning S-wave scattering phase shifts bypassing the radial Schrödinger equation

  title={Machine learning S-wave scattering phase shifts bypassing the radial Schr{\"o}dinger equation},
  author={Alessandro Romualdi and Gionni Marchetti},
  journal={The European Physical Journal B},
We present a proof of concept machine learning model resting on a convolutional neural network capable of yielding accurate scattering s-wave phase shifts caused by different three-dimensional spherically symmetric potentials at fixed collision energy thereby bypassing the radial Schrödinger equation. In our work, we discuss how the Hamiltonian can serve as a guiding principle in the construction of a physically-motivated descriptor. The good performance, even in presence of bound states in the… 
1 Citations

Estimating scattering potentials in inverse problems with Volterra series and neural networks

  • G. Balassa
  • Mathematics
    The European Physical Journal A
  • 2022
Inverse problems often occur in nuclear physics, when an unknown potential has to be determined from the measured cross sections, phase shifts or other observables. In this paper, a data-driven



Deep-neural-network solution of the electronic Schrödinger equation

High-accuracy quantum chemistry methods struggle with a combinatorial explosion of Slater determinants in larger molecular systems, but now a method has been developed that learns electronic wavefunctions with deep neural networks and reaches high accuracy with only a few determinants.

Phase shifts of the three‐dimensional spherically symmetric square well potential

Although the general properties of the phase shift of the three‐dimensional spherically symmetrical square well potential are described in most textbooks on quantum mechanics, specific graphical

Machine learning for the solution of the Schrödinger equation

  • S. Manzhos
  • Computer Science
    Mach. Learn. Sci. Technol.
  • 2020
This work surveys recent uses of ML techniques to solve the Schrödinger equation, including the vibrational Schr Ödinger equations, the electronic SchröDinger equation and the related problems of constructing functionals for density functional theory (DFT) as well as potentials which enter semi-empirical approximations to DFT.

Machine learning phases of matter

It is shown that modern machine learning architectures, such as fully connected and convolutional neural networks, can identify phases and phase transitions in a variety of condensed-matter Hamiltonians.

The absolute definition of the phase-shift in potential scattering

The variable phase approach to potential scattering with regular spherically symmetric potentials satisfying Eq. (1), and studied by Calogero in his book [Variable Phase Approach to Potential

From Lippmann-Schwinger formulations to a general formula for absolute asymptotic scattering phase functions and shifts: a unified framework for potentials of any range

Appropriately handling the Lippmann-Schwinger equation can bring substantial benefits in quantum scattering. Here, the advantages of a parametric equation for the system's normalised wavefunction, ψ,

Perspective: Machine learning potentials for atomistic simulations.

  • J. Behler
  • Materials Science
    The Journal of chemical physics
  • 2016
Recent advances in machine learning (ML) now offer an alternative approach for the representation of potential-energy surfaces by fitting large data sets from electronic structure calculations, which are reviewed along with a discussion of their current applicability and limitations.

Nonrelativistic Quantum Mechanics

The Breakdown of Classical Mechanics Review of Classical Mechanics Elementary Systems One-Dimensional Problems More One-Dimensional Problems Mathematical Foundations Physical Interpretation