This paper is concerned with the numerical analysis of linear and nonlinear Schr{\"o}dinger equations with analytic potentials. While the regularity of the potential (and the source term when there is one) automatically conveys to the solution in the linear cases, this is no longer true in general in the nonlinear case. We also study the rate of convergence of the planewave (Fourier) discretization method for computing numerical approximations of the solution.

翻译：本文致力于含解析势的线性和非线性薛定谔方程的数值分析。在线性情形下，势函数（以及存在源项时的源项）的正则性会自动传递至解，但在非线性情形下，这一性质通常不再成立。我们还研究了平面波（傅里叶）离散化方法用于计算解的数值逼近时的收敛速率。