A numerical method for the fractional Schrödinger type equation of spatial dimension two
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This work focuses on an investigation of the (n+1)-dimensional time-dependent fractional Schrödinger type equation. In the early part of the paper, the wave function is obtained using Laplace and Fourier transform methods and a symbolic operational form of the solutions in terms of Mittag-Leffler functions is provided. We present an expression for the wave function and for the quantum mechanical probability density. We introduce a numerical method to solve the case where the space component has dimension two. Stability conditions for the numerical scheme are obtained.
Key Words and Phrasesfractional partial differential equation fractional Schrödinger equation finite difference method stability Mittag-Leffler function
MSC 2010Primary 35R11 Secondary 42A38, 33E12, 65M06, 47H10
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