A note on the Schrödinger smoothing effect
Sign Up to like & getrecommendations! Published in 2019 at "Mathematische Nachrichten"
DOI: 10.1002/mana.201800502
Abstract: The Kato–Yajima smoothing estimate is a smoothing weighted L2 estimate with a singular power weight for the Schrödinger propagator. The weight has been generalized relatively recently to Morrey–Campanato weights. In this paper we make this… read more here.
Keywords: schr; note schr; dinger smoothing; schr dinger ... See more keywords
Transmutation Operators Associated With an Angular SchröDinger‐Type Operator
Sign Up to like & getrecommendations! Published in 2025 at "Mathematical Methods in the Applied Sciences"
DOI: 10.1002/mma.11124
Abstract: In this work, we study the time‐independent homogeneous Schrödinger equation Δ−q(θ)r2u=0$$ \left(\Delta -\frac{q\left(\theta \right)}{r^2}\right)u=0 $$ in a bounded domain Ω⊂ℂ$$ \Omega \subset \mathbb{C} $$ . We assume the potential q$$ q $$ is a continuously… read more here.
Keywords: operator; schr dinger; schr; transmutation ... See more keywords
Bourgain’s Counterexample in the Sequential Convergence Problem for the Schrödinger Equation
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DOI: 10.1007/s00041-025-10162-x
Abstract: We study the problem of pointwise convergence for the Schrödinger operator on Rn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {R}}^n$$\end{document} along time sequences. We show that the sharp counterexample to the sequential… read more here.
Keywords: schr dinger; problem; schr; convergence ... See more keywords
Decay of the stochastic linear Schrödinger equation in $$d \ge 3$$ d ≥ 3 with small multiplicative noise
Sign Up to like & getrecommendations! Published in 2018 at "Stochastics and Partial Differential Equations: Analysis and Computations"
DOI: 10.1007/s40072-020-00172-9
Abstract: We give decay estimates of the solution to the linear Schrödinger equation in dimension $$d \ge 3$$ d ≥ 3 with a small noise which is white in time and colored in space. As a… read more here.
Keywords: dinger equation; decay; schr; linear schr ... See more keywords
Continuity of the spectrum of quasi-periodic Schrödinger operators with finitely differentiable potentials
Sign Up to like & getrecommendations! Published in 2020 at "Ergodic Theory and Dynamical Systems"
DOI: 10.1017/etds.2018.48
Abstract: In this paper, we consider the spectrum of discrete quasi-periodic Schrödinger operators on $\ell ^{2}(\mathbb{Z})$ with the potentials $v\in C^{k}(\mathbb{T})$ . For sufficiently large $k$ , we show that the Lebesgue measure of the spectrum… read more here.
Keywords: periodic schr; schr; quasi periodic; schr dinger ... See more keywords
SchrödingerNet: A Universal Neural Network Solver for the Schrödinger Equation.
Sign Up to like & getrecommendations! Published in 2024 at "Journal of chemical theory and computation"
DOI: 10.1021/acs.jctc.4c01287
Abstract: Recent advances in machine learning have facilitated numerically accurate solution of the electronic Schrödinger equation (SE) by integrating various neural network (NN)-based wave function ansatzes with variational Monte Carlo methods. Nevertheless, such NN-based methods are… read more here.
Keywords: schr dinger; schr dingernet; schr; dinger equation ... See more keywords
The Schrödinger’s cat stage of the pandemic
Sign Up to like & getrecommendations! Published in 2022 at "Education for Primary Care"
DOI: 10.1080/14739879.2022.2090862
Abstract: What I’m about to describe is very much focused on the United Kingdom. However, readers in countries across the world who are not currently facing the same situation will quite possibly be doing so sometime… read more here.
Keywords: educator; dinger cat; schr; schr dinger ... See more keywords
Existence and stability results for time-fractional Schrödinger equations Related to the harmonic oscillator
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DOI: 10.1088/1402-4896/ad9eea
Abstract: The implications of the Schrödinger equation is profound, revealing the wave-particle duality of matter, the concept of superposition, and the probabilistic nature of quantum measurements. Its solutions provide critical insights into the behavior of atoms,… read more here.
Keywords: schr dinger; schr; harmonic oscillator; related harmonic ... See more keywords
Semiclassical cosmology with backreaction: The Friedmann-Schrödinger equation and inflation
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DOI: 10.1103/physrevd.99.086018
Abstract: We propose and study a semi-classical cosmological system akin to the Newton-Schr\"odinger equation where matter field evolution is determined by time dependent Schr\"odinger equation. The resulting dynamics is one where the scale factor self-consistently informs… read more here.
Keywords: inflation; scalar field; equation; schr ... See more keywords
Optical solutions to conformable nonlinear Schrödinger equation with cubic–quintic–septimal in weakly non-local media by new Kudryashov approach
Sign Up to like & getrecommendations! Published in 2024 at "Modern Physics Letters B"
DOI: 10.1142/s0217984925500630
Abstract: This paper analyzes the cubic–quintic–septimal nonlinear Schrödinger equation with conformable derivative utilizing the new Kudryashov approach. Through this algorithm, several exact solutions are constructed within the present nonlinear conformable Schrödinger model such as bell-shaped, singular,… read more here.
Keywords: equation; schr dinger; schr; cubic quintic ... See more keywords