The SPF Method For The Time-depending Solutions Of Nano Scale Systems

Nano scale science and technology is a sign of advanced technology in the 21st century. The nanometer materials have a lot of special properties: quantum size effect, surface effect and macroscopic quantum tunneling effect etc..So the study and development about nanometer materials increase everyday.Nano scale science and technology is a subject between 0.1nm and 100nm. It studys the law of motion of atoms and molecules. So we must use the quantum mechanics instead of the Newtonian mechanics. So, study the nanometer materials first use the quantum mechanics and then use the compute method bases on the quantum mechanics. In order to compute the electron structure in nanometer materials, we have to solve the electron Shr?dinger equation exactly. We can't solve it exactly at most situation unless use computer. So in this article we choosed the appropriate simulate method to simulate the two-dimensional nanometer system in real-space by the computer program. Even use computer to solve the time-dependent Schr?dinger equation, there are a lot of problems to be considered. Because even to a single particle moving in non-trivial potential field is not a simple matter. The dimension of the matrix representing H is quite large,we haven't so much RAM to stone the date, and the CPU time, explicit and unconditionally stable are must be considered either. The SPF method is developed recently, it satisfies all the requirements above.In this article, we introduced the principle of SPF and the advantage in this method of different order, and solved the time-dependent Shr?dinger equation. We made out a program of the SPF method, and first validated the interference phenophase of Bose-Einstein condensation. We simulated the interference pattern of same particles successful. By changing the parameters in the equation,we can simulate many different situations such as interference pattern of different particles. So the program we mada is correct. And then we researched the 2-dimension system which had regular distribution square potential energy of Nano scale. At different square potential energy ,we change the width and the hight of the potential energy to see how the (ψt )2 changed. And gave the picture of the result.Scanning Tunneling Microscopy(STM)shows the surface wave function of the material. As we can derive the pictures of the wave function of 2-dimension Nano scale system, we can predict some characters of Nano scale material, and then validate it by STM.