Solutions Of Schrodinger Equation Under Diferent Conditions

Schro¨dinger equation originated in the1920s. It is a basic equation and a basicssumption in quantum mechanics. Its correctness can only rely on experiments tost. It reveals the basic law of physical movement in the physical world. Just as thele of Newtonian law in classical mechanics, it is a powerful tool which deals withll non-relativistic problems in atomic physics. It is widely used in atomic, molecular,lid state physics, nuclear physics, chemistry and other fields. And it has been deeplyeveloped until now. Academician Guo Bailing believes that nonlinear Schrodingerquation is a very important kind of nonlinear dispersive wave equations. He introducesose Einstein condensation problems and strange-wave problems. He also elaboratese new development of the research on nonlinear Schrodinger equation.In this paper, we use Variational methods, strong sandwich pairs and the localnking theorem to study the existence of solutions for Schr¨odinger equation.The thesis is divided into three chapters according to the contents.In chapter1, we introduce some fundamental knowledges and source of theory.In chapter2, we mainly discuss a class of Schro¨dinger equation as following where f (x, u) be a Carath′eodory function on RN×Râ†'R and the potential V satisfiesWe conclude the existence of nontrivial solutions of Schrodinger equation using thelocal linking theorem.