Experimental realisations of the fractional Schrödinger equation in the temporal domain. [PDF]
Nat Commun, 2023 Studies on the fractional Schrödinger equation (FSE) remain mostly theoretical, due to the lack of materials supporting fractional dispersion or diffraction.
Liu S, Zhang Y, Malomed BA, Karimi E.
europepmc +3 more sources
Carroll–Schrödinger equation as the ultra-relativistic limit of the tachyon equation [PDF]
Scientific ReportsThe Poincaré symmetry can be contracted in two ways to yield the Galilei symmetry and the Carroll symmetry. The well-known Schrödinger equation exhibits the Galilei symmetry and is a fundamental equation in Galilean quantum mechanics.
Mojtaba Najafizadeh
doaj +2 more sources
Rogue periodic waves of the focusing nonlinear Schrödinger equation. [PDF]
Proc Math Phys Eng Sci, 2018 Rogue periodic waves stand for rogue waves on a periodic background. The nonlinear Schrödinger equation in the focusing case admits two families of periodic wave solutions expressed by the Jacobian elliptic functions dn and cn.
Chen J, Pelinovsky DE.
europepmc +3 more sources
Numerical simulation of the space dependent fractional Schrödinger equation for London dispersion potential type [PDF]
Heliyon, 2020 In this study, we apply the definition of one of the fractional derivatives definitions of increasing values of the variable, which is the fractional derivative of Riemann-Liouville, and the numerical-integral methods to find numerical solutions of the ...
Marwan Al-Raeei, Moustafa Sayem El-Daher
doaj +2 more sources
Multiple normalized solutions for a Sobolev critical Schrödinger equation [PDF]
Mathematische Annalen, 2020 We study the existence of standing waves, of prescribed L2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength ...
L. Jeanjean, Thanh Trung Le
semanticscholar +1 more source
QuantumFDTD - A computational framework for the relativistic Schrödinger equation [PDF]
EPJ Web of Conferences, 2022 We extend the publicly available quantumfdtd code. It was originally intended for solving the time-independent three-dimensional Schrödinger equation via the finite-difference time-domain (FDTD) method and for extracting the ground, first, and second ...
Delgado Rafael L. +3 more
doaj +1 more source
Recursive Schrödinger equation approach to faster converging path integrals [PDF]
Physical Review E, 2009 By recursively solving the underlying Schr\" odinger equation, we set up an efficient systematic approach for deriving analytic expressions for discretized effective actions. With this we obtain discrete short-time propagators for both one and many particles in arbitrary dimension to orders which have not been accessible before.
Antun Balaz +4 more
openaire +5 more sources
Deep-neural-network solution of the electronic Schrödinger equation [PDF]
Nature Chemistry, 2019 The electronic Schrödinger equation can only be solved analytically for the hydrogen atom, and the numerically exact full configuration-interaction method is exponentially expensive in the number of electrons.
J. Hermann, Zeno Schätzle, F. Noé
semanticscholar +1 more source
Ab-Initio Solution of the Many-Electron Schrödinger Equation with Deep Neural Networks [PDF]
Physical Review Research, 2019 Given access to accurate solutions of the many-electron Schr\"odinger equation, nearly all chemistry could be derived from first principles. Exact wavefunctions of interesting chemical systems are out of reach because they are NP-hard to compute in ...
David Pfau +3 more
semanticscholar +1 more source
Schrödinger–Newton Equation with Spontaneous Wave Function Collapse
Quantum Reports, 2022 Based on the assumption that the standard Schrödinger equation becomes gravitationally modified for massive macroscopic objects, two independent proposals have survived from the 1980s.
Lajos Diósi
doaj +1 more source