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 $L^2-$ 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.

在本文中，我们集中于一种数值方法，用于计算分数阶平稳薛定ding方程（FSSE）的基态。我们首先构造一个连续的归一化分数梯度流（CNFGF）并证明其${\mathrm{大号}}^2-$规范守恒和减少能量的特性。然后，我们引入具有离散归一化的分数梯度流（FGFDN）来求解CNFGF，并通过Crank-Nicolson（CN）傅里叶伪谱方法给出了完全离散化的方案。并在线性情况下证明了全离散方案的能量递减特性。最后，我们进行数值实验以证明我们数值方法的有效性。