The Numerical Method For Schr(o|¨)nger Equation Based On Meshless Method

Schro¨nger equation is a basic function in the quantum mechanics which is proposedby Schro¨nger, and it is a kind of partial diferential equation(PDE) combining conceptionof material wave with wave equation. Schro¨nger equation reveals basic law of materialmotion in the micro-physics world, and is extensively applied in the atom,fraction,solidphysics,nuclear physics,chemistry and other fields.Therefore,the discussion of the equa-tion has important theoretical and practical significance.Meshless methods are relatively new numerical algorithms for the simulation ofphysical phenomena.In recent years,meshless methods have been extensively applied toproblems in fluid dynamics,solid mechanics, and other fields.In this dissertation, two ver-sions of meshless methods, Kansa’s Method and Particular Solution Method(MPS), havebeen developed and applied to solving Schro¨nger equation.And the valid of methods areproved in this work.Traditional simulation algorithms, such as the Finite Diference Method(FDM),theFinite Element Method(FEM) and the Boundary Element Method(BEM),have achievedgreat success in many branches of engineering and the sciences during the past severalyears.These mesh based methods will continue to play central roles in the future,but theyall require that a mesh or grid be generated for the domain as part of the solution pro-cess.Meshless method, in contrast,use the geometry of the domain directly to avoid manyof difculties.