Fourier pseudospectral method for fractional stationary Schrödinger equation
DOI10.1016/J.APNUM.2021.02.008zbMath1468.35189OpenAlexW3129511390WikidataQ112880260 ScholiaQ112880260MaRDI QIDQ2029113
Ai-Guo Xiao, Yin Yang, Xueyang Li
Publication date: 3 June 2021
Published in: Applied Numerical Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.apnum.2021.02.008
ground stateFourier pseudospectral methodfractional Schrödinger equationcontinuous normalized fractional gradient flowenergy diminishing
Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) NLS equations (nonlinear Schrödinger equations) (35Q55) PDEs in connection with quantum mechanics (35Q40) Numerical methods for discrete and fast Fourier transforms (65T50) Fractional partial differential equations (35R11)
Cites Work
- Unnamed Item
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- A one-dimensional model for dispersive wave turbulence
- Eigenvalues of the fractional Laplace operator in the interval
- Efficient and spectrally accurate numerical methods for computing ground and first excited states in Bose-Einstein condensates
- Existence of weak solutions for a fractional Schrödinger equation
- Fractional quantum mechanics and Lévy path integrals
- On the ground states and dynamics of space fractional nonlinear Schrödinger/Gross-Pitaevskii equations with rotation term and nonlocal nonlinear interactions
- Anti-symmetry of the second eigenfunction of the fractional Laplace operator in a 3-D ball
- The Cauchy process and the Steklov problem
- On the continuum limit for discrete NLS with long-range lattice interactions
- Mathematical theory and numerical methods for Bose-Einstein condensation
- Mass-conservative Fourier spectral methods for solving the fractional nonlinear Schrödinger equation
- Conservative Fourier spectral method and numerical investigation of space fractional Klein-Gordon-Schrödinger equations
- Fractional calculus for power functions and eigenvalues of the fractional Laplacian
- Solving fractional Schrödinger-type spectral problems: Cauchy oscillator and Cauchy well
- A Mass and Magnetization Conservative and Energy-Diminishing Numerical Method for Computing Ground State of Spin-1 Bose–Einstein Condensates
- Computing the Ground State Solution of Bose--Einstein Condensates by a Normalized Gradient Flow
- Ground States and Dynamics of Multicomponent Bose--Einstein Condensates
- Crank–Nicolson Fourier spectral methods for the space fractional nonlinear Schrödinger equation and its parameter estimation
- Eigenvalues of the fractional Laplace operator in the unit ball
- Computing the Ground and First Excited States of the Fractional Schrödinger Equation in an Infinite Potential Well
- Ground state solutions for nonlinear fractional Schrödinger equations in $\mathbb {R}^N$RN
- Ground state solutions of asymptotically linear fractional Schrödinger equations
- Numerical approximations of a norm-preserving gradient flow and applications to an optimal partition problem
- Wave turbulence in one-dimensional models
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