Abstract
In this paper, we focus on a numerical method for computing the ground state of the fractional stationary Schrödinger equation (FSSE). We first construct a continuous normalized fractional gradient flow (CNFGF) and prove its L2− norm conservation and energy diminishing properties. Then we introduce the fractional gradient flow with discrete normalization (FGFDN) to solve the CNFGF, and give the fully discretized scheme by Crank-Nicolson (CN) Fourier pseudospectral method. And the energy diminishing property of the fully discretized scheme is proved in linear case. Finally, we conduct numerical experiments to demonstrate the efficiency of our numerical method.
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