不同非局部系数的薛定谔方程特征研究

Research on the characteristics of Schr dinger equation with different nonlocal coefficients

研究带有不同类型非局部积分项系数的Schr dinger方程,通过代数分析方法结合微分方程的谱理论将解的存在性转换为代数方程解的存在性,并给出一维情形解曲线的几何图形。相对已有文献解的存在性研究而言,利用更简单的方法得到了较好的结果,同时以微分方程解曲线的图示作为辅助,促进理论与实际的结合。

This paper considered the Schr dinger equation with different types of nonlocal integral term coefficients.By using the algebraic analysis method and the spectrum theory of differential equations,the existence of solutions was transformed into the existence of roots for some algebraic equations,the shape of the corresponding curve for the solution of the one-dimensional case.Compared with the results on the existence of solutions in the references,improved results were derived with the help of simpler methods.In order to promote the combination of theory and practice,as the auxiliaries,some curves of solutions were set in the progress of proving main results.