Generalized fractional Schrödinger equation with space-time fractional derivatives

2007 ◽  
Vol 48 (4) ◽  
pp. 043502 ◽  
Author(s):  
Shaowei Wang ◽  
Mingyu Xu
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Fractional Derivatives ◽  
Space Time ◽  
Fractional Schrödinger Equation ◽  
Fractional Schrodinger Equation

Efficient exponential time differencing methods with Padé approximations for the semilinear space-time-fractional Schrödinger equation

2020 ◽  
pp. 2050428
Author(s):  
Xiao Liang
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Space Time ◽  
Padé Approximations ◽  
Exponential Time ◽  
Fractional Schrödinger Equation ◽  
Exponential Time Differencing ◽  
Pade Approximations ◽  
Semilinear Space ◽  
Fractional Schrodinger Equation

The semilinear space-time-fractional Schrödinger equation is solved numerically using one-step and two-step exponential time differencing methods in time, and a fractional centered difference scheme in space. The two-parametric Mittag–Leffler function arising in the time integral is computed with Padé approximations, which improves the efficiency of the scheme markedly. Numerical experiments for well-known models from literature are performed to show the effectiveness and efficiency of the proposed methods.

Space-Time Fractional Schrödinger Equation With Composite Time Fractional Derivative

2015 ◽  
Vol 18 (5) ◽  
Author(s):  
Johan L.A. Dubbeldam ◽  
Zivorad Tomovski ◽  
Trifce Sandev
Keyword(s):  
Schrödinger Equation ◽  
Fractional Derivative ◽  
Schrodinger Equation ◽  
Time Derivative ◽  
Adomian Decomposition Method ◽  
Space Time ◽  
Infinite Domain ◽  
Fractional Schrödinger Equation ◽  
Adomian Decomposition ◽  
Fractional Schrodinger Equation

AbstractThe fractional Schrödinger equation has recently received substantial attention. We generalize the fractional Schrödinger equation to the Hilfer time derivative and the Caputo space derivative, and solve this equation for an infinite potential by using the Adomian decomposition method. The infinite domain solution of the space-time fractional Schrödinger equation in the case of Riesz space fractional derivative is obtained in terms of the Fox H-functions. We interpret our results for the fractional Schrödinger equation by introducing a complex effective potential in the standard Schrödinger equation, which can be used to describe quantum transport in quantum dots.

scholarly journals Fractional schrödinger equation with zero and linear potentials

2016 ◽  
Vol 19 (4) ◽  
Author(s):  
Saleh Baqer ◽  
Lyubomir Boyadjiev
Keyword(s):  
Schrödinger Equation ◽  
Potential Field ◽  
Schrodinger Equation ◽  
Fractional Derivatives ◽  
Free Particle ◽  
Linear Potential ◽  
Fractional Schrödinger Equation ◽  
Zero Potential ◽  
Fractional Schrodinger Equation

AbstractThis paper is about the fractional Schrödinger equation expressed in terms of the Caputo time-fractional and quantum Riesz-Feller space fractional derivatives for particle moving in a potential field. The cases of free particle (zero potential) and a linear potential are considered. For free particle, the solution is obtained in terms of the Fox

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