Ground states for a linearly coupled indefinite Schrödinger system with steep potential well

2021 ◽  
Vol 62 (8) ◽  
pp. 081505
Author(s):  
Ying-Chieh Lin ◽  
Kuan-Hsiang Wang ◽  
Tsung-fang Wu
Keyword(s):  
Ground States ◽  
Potential Well ◽  
Steep Potential Well ◽  
Schrödinger System

Ground state solutions for Klein–Gordon–Maxwell system with steep potential well

2019 ◽  
Vol 90 ◽  
pp. 175-180 ◽  
Author(s):  
Xiao-Qi Liu ◽  
Shang-Jie Chen ◽  
Chun-Lei Tang
Keyword(s):  
Ground State ◽  
Potential Well ◽  
Maxwell System ◽  
Ground State Solutions ◽  
Klein Gordon ◽  
Steep Potential Well

Steep potential well may help Kirchhoff type equations to generate multiple solutions

2020 ◽  
Vol 190 ◽  
pp. 111609 ◽  
Author(s):  
Juntao Sun ◽  
Tsung-fang Wu
Keyword(s):  
Multiple Solutions ◽  
Potential Well ◽  
Kirchhoff Type ◽  
Steep Potential Well

scholarly journals Lévy Flights in a Steep Potential Well

2004 ◽  
Vol 115 (5/6) ◽  
pp. 1505-1535 ◽  
Author(s):  
Aleksei V. Chechkin ◽  
Vsevolod Yu. Gonchar ◽  
Joseph Klafter ◽  
Ralf Metzler ◽  
Leonid V. Tanatarov
Keyword(s):  
Potential Well ◽  
Lévy Flights ◽  
Levy Flights ◽  
Steep Potential Well

Dancer–Fuc̆ik spectrum for fractional Schrödinger operators with a steep potential well on RN

2019 ◽  
Vol 189 ◽  
pp. 111565 ◽  
Author(s):  
Zhisu Liu ◽  
Haijun Luo ◽  
Zhitao Zhang
Keyword(s):  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
Potential Well ◽  
Steep Potential Well

scholarly journals Computing the Ground and First Excited States of the Fractional Schrödinger Equation in an Infinite Potential Well

2015 ◽  
Vol 18 (2) ◽  
pp. 321-350 ◽  
Author(s):  
Siwei Duo ◽  
Yanzhi Zhang
Keyword(s):  
Schrödinger Equation ◽  
Excited States ◽  
Schrodinger Equation ◽  
Fractional Laplacian ◽  
Ground States ◽  
Euler Method ◽  
Potential Well ◽  
Fractional Schrödinger Equation ◽  
Fractional Schrodinger Equation ◽  
Infinite Potential Well

AbstractIn this paper, we numerically study the ground and first excited states of the fractional Schrödinger equation in an infinite potential well. Due to the nonlocality of the fractional Laplacian, it is challenging to find the eigenvalues and eigenfunctions of the fractional Schrödinger equation analytically. We first introduce a normalized fractional gradient flow and then discretize it by a quadrature rule method in space and the semi-implicit Euler method in time. Our numerical results suggest that the eigenfunctions of the fractional Schrödinger equation in an infinite potential well differ from those of the standard (non-fractional) Schrödinger equation. We find that the strong nonlocal interactions represented by the fractional Laplacian can lead to a large scattering of particles inside of the potential well. Compared to the ground states, the scattering of particles in the first excited states is larger. Furthermore, boundary layers emerge in the ground states and additionally inner layers exist in the first excited states of the fractional nonlinear Schrödinger equation. Our simulated eigenvalues are consistent with the lower and upper bound estimates in the literature.

Sign in / Sign up

Export Citation Format

Share Document