Generalized fractional Schrödinger equation with space-time fractional derivatives

From MaRDI portal

Publication:3442277

Jump to:navigation, search

DOI10.1063/1.2716203zbMath1137.81328OpenAlexW2074080929MaRDI QIDQ3442277

Shaowei Wang, Mingyu Xu

Publication date: 16 May 2007

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.2716203

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Fractional derivatives and integrals (26A33) PDEs in connection with quantum mechanics (35Q40)

Related Items

Convergence analysis of an L1-continuous Galerkin method for nonlinear time-space fractional Schrödinger equations ⋮ Error analysis of the unstructured mesh finite element method for the two-dimensional time-space fractional Schrödinger equation with a time-independent potential ⋮ A high-order scheme for time-space fractional diffusion equations with Caputo-Riesz derivatives ⋮ Extremal solutions of \(\varphi\)-Caputo fractional evolution equations involving integral kernels ⋮ Green's function of time fractional diffusion equation and its applications in fractional quantum mechanics ⋮ The fractional dynamics of quantum systems ⋮ Fractional corresponding operator in quantum mechanics and applications: A uniform fractional Schrödinger equation in form and fractional quantization methods ⋮ Numerical analysis for time-fractional Schrödinger equation on two space dimensions ⋮ Controlling Bifurcations in Fractional-Delay Systems with Colored Noise ⋮ An improved collocation method for multi-dimensional space-time variable-order fractional Schrödinger equations ⋮ Solution of Sakata-Taketani equation via the Caputo and Riemann-Liouville fractional derivatives ⋮ Lévy path integrals of particle on circle and some applications ⋮ Dynamic analysis of a fractional-order Lorenz chaotic system ⋮ Time fractional quantum mechanics ⋮ On distributions of functionals of anomalous diffusion paths ⋮ On the ground states and dynamics of space fractional nonlinear Schrödinger/Gross-Pitaevskii equations with rotation term and nonlocal nonlinear interactions ⋮ Shehu transform on time-fractional Schrödinger equations -- an analytical approach ⋮ A second-order finite difference scheme for the multi-dimensional nonlinear time-fractional Schrödinger equation ⋮ Analytical solution of the space-time fractional nonlinear Schrödinger equation ⋮ New analysis and application of fractional order Schrödinger equation using with Atangana–Batogna numerical scheme ⋮ Two competent novel techniques based on two-dimensional wavelets for nonlinear variable-order Riesz space-fractional Schrödinger equations ⋮ Linearized Crank-Nicolson scheme for the nonlinear time-space fractional Schrödinger equations ⋮ Stability and convergence of the space fractional variable-order Schrödinger equation ⋮ The asymptotic behavior of the time fractional Schrödinger equation on Hilbert space ⋮ Quantum tunneling from family of Cantor potentials in fractional quantum mechanics ⋮ Unconditionally Convergent $L1$-Galerkin FEMs for Nonlinear Time-Fractional Schrödinger Equations ⋮ Fractional Schrödinger equation and time dependent potentials ⋮ The numerical computation of the time fractional Schrödinger equation on an unbounded domain ⋮ Combined Galerkin spectral/finite difference method over graded meshes for the generalized nonlinear fractional Schrödinger equation ⋮ A fast implicit difference scheme for solving high-dimensional time-space fractional nonlinear Schrödinger equation ⋮ Normalized fractional gradient flow for nonlinear Schrödinger/Gross-Pitaevskii equations ⋮ Linearized Transformed $L1$ Galerkin FEMs with Unconditional Convergence for Nonlinear Time Fractional Schrödinger Equations ⋮ A second-order \(L2\)-\(1_\sigma\) difference scheme for the nonlinear time-space fractional Schrödinger equation ⋮ Fractional-time Schrödinger equation: fractional dynamics on a comb ⋮ Existence of solutions for a fractional derivative system of equations ⋮ Time independent fractional Schrödinger equation for generalized Mie-type potential in higher dimension framed with Jumarie type fractional derivative ⋮ Reanalysis of an open problem associated with the fractional Schrödinger equation ⋮ The transition of energy and bound states in the continuum of fractional Schrödinger equation in gravitational field and the effect of the minimal length ⋮ Optimal error analysis of the alikhanov formula for a time-fractional Schrödinger equation ⋮ The ground states for theNcoupled nonlinear fractional Schrödinger equations ⋮ Quantization method and Schrödinger equation of fractional time and their weak effects on Hamiltonian: phase transitions of energy and wave functions ⋮ Some solutions to the space fractional Schrödinger equation using momentum representation method ⋮ The global solution for a class of systems of fractional nonlinear Schrödinger equations with periodic boundary condition ⋮ Analytic and approximate solutions of the space-time fractional Schrödinger equations by homotopy perturbation Sumudu transform method ⋮ Space-time fractional Schrödinger equation with time-independent potentials ⋮ Solutions for a Schrödinger equation with a nonlocal term ⋮ Fractional Green's function for the time-dependent scattering problem in the space-time-fractional quantum mechanics ⋮ Fractional Schrödinger equation for a particle moving in a potential well ⋮ Time fractional Schrödinger equation: Fox's H-functions and the effective potential ⋮ A numerical method for fractional Schrödinger equation of Lennard-Jones potential ⋮ Unnamed Item ⋮ Numerical Simulation for the Variable-Order Fractional Schrödinger Equation with the Quantum Riesz-Feller Derivative ⋮ A second-order implicit difference scheme for the nonlinear time-space fractional Schrödinger equation ⋮ Taming stochastic bifurcations in fractional-order systems via noise and delayed feedback ⋮ Numerical simulation of multi-dimensional distributed-order generalized Schrödinger equations ⋮ Efficient Numerical Computation of Time-Fractional Nonlinear Schrödinger Equations in Unbounded Domain ⋮ Asymptotic expansions and approximations for the Caputo derivative ⋮ Time fractional Schrödinger equation revisited ⋮ Fractional Schrödinger equation with noninteger dimensions ⋮ Scattering problems in the fractional quantum mechanics governed by the 2D space-fractional Schrödinger equation ⋮ The effect of time fractality on the transition coefficients: historical Stern-Gerlach experiment revisited ⋮ Geometry and field theory in multi-fractional spacetime ⋮ The space fractional diffusion equation with Feller's operator ⋮ A fractional Schrödinger equation and its solution ⋮ Applications of density matrix in the fractional quantum mechanics: Thomas-Fermi model and Hohenberg-Kohn theorems revisited ⋮ Analysis of time fractional and space nonlocal stochastic nonlinear Schrödinger equation driven by multiplicative white noise ⋮ Unnamed Item ⋮ Green’s functions and energy eigenvalues for delta-perturbed space-fractional quantum systems ⋮ The global analysis on the spectral collocation method for time fractional Schrödinger equation ⋮ On the numerical solution of the eigenvalue problem in fractional quantum mechanics ⋮ Time and Space Fractional Schrödinger Equation with Fractional Factor ⋮ New approaches for the solution of space-time fractional Schrödinger equation ⋮ Fast L2-1\(_\sigma\) Galerkin FEMs for generalized nonlinear coupled Schrödinger equations with Caputo derivatives ⋮ The time independent fractional Schrödinger equation with position-dependent mass ⋮ A Schwarz waveform relaxation method for time-dependent space fractional Schrödinger/heat equations ⋮ Applications of continuity and discontinuity of a fractional derivative of the wave functions to fractional quantum mechanics ⋮ Fractional Schrödinger equation in gravitational optics ⋮ Broadening quantum cosmology with a fractional whirl ⋮ Time fractional development of quantum systems ⋮ Bound state for the fractional Schrödinger equation with unbounded potential ⋮ Infinitely many solutions of fractional Schrödinger–Maxwell equations ⋮ Infinite wall in the fractional quantum mechanics ⋮ Time fractional Schrödinger equation with a limit based fractional derivative ⋮ ON THE NUMERICAL SIMULATION OF TIME-SPACE FRACTIONAL COUPLED NONLINEAR SCHRÖDINGER EQUATIONS UTILIZING WENDLAND’S COMPACTLY SUPPORTED FUNCTION COLLOCATION METHOD ⋮ Green's function for the time-dependent scattering problem in the fractional quantum mechanics ⋮ Exact solutions of fractional Schrödinger-like equation with a nonlocal term ⋮ Quantum mechanics in fractional and other anomalous spacetimes ⋮ Generalized fractional algebraic linear system solvers ⋮ On the numerical solution and dynamical laws of nonlinear fractional Schrödinger/Gross–Pitaevskii equations ⋮ Solving a nonlinear fractional Schrödinger equation using cubic B-splines ⋮ Error analysis of a fully discrete scheme for time fractional Schrödinger equation with initial singularity

Cites Work

Retrieved from "https://portal.mardi4nfdi.de/w/index.php?title=Publication:3442277&oldid=16755765"