Location:Home > Neo-confucianism > Physics > Theoretical Physics > The Schrodinger particle motion in two-dimensional systems
Details
Name

The Schrodinger particle motion in two-dimensional systems

Downloads: []
Author
Tutor: LiuHong
School: Nanjing Normal University
Course: Theoretical Physics
Keywords: Schrodinger equation,split operator,finite difference,wave packetmotion,step bar
CLC: O413.1
Type: Master's thesis
Year:  2013
Facebook Google+ Email Gmail Evernote LinkedIn Twitter Addthis

not access Image Error Other errors

Abstract:
In quantum mechanics, the dynamic of microscopic particles is described by the wave function that is determined by the Schrodinger equation. Microscopic particles have the particle character and wave character. The dynamical characters of microscopic particles in the nano-sized materials is different from those in the macroscopic sizes. With the development of modern science and technology, especially since the discovery of single-layer graphene, a variety of nano-sized devices have been porposed and producted one after another, and a variety of new quantum effects have also been observed. In recent years, the dynamical behavior of microscopic particles in nano-sized materials by using the time-dependent Schrodinger equation attracted more and more attention and become the research focus.In the present thesis, we combine the split-operator method with the CN method to solve the time-dependent Schrodinger equation, and to study the dynamical behavior of wave packet of the particale in the two-dimensional electron gas. We study the relationship among the character parameters of wave packet, the transmission and distribution of particle as well as the system size.First of all, we realize the numerical solution of the time-dependent Schrodinger equation in the two-dimensional system, by using the combined method of the effective split-operator method and CN method. In the program of numerical calculation, we adopt the recursive iterative method to do with the considerably large size two-dimensional system.Secondly, on the basis of numerical program, we calculate the transmission of the wave packet into the area with higher potential to study the factors that can influence on the dynamical behavior of microscopic particles, such as the height of barriers, the energy and the width of package. We find that the wave packet with large package width presents a remarkable particle character, on the contrary, the wave packet with small package width presents a remarkable wave character. The transmission of the wave packet with small package width is higher than that for large package width due to the stronger wave character for small package width. The transmission of the wave packet increases with the package energy. The results in the present here are in an agreement with the previous calculation results. Furthermore, we give a clear explanation and description of wave packet in this system.Finally, we try to investigate the transmission behavior of microscopic particles in the nano-sized system with a narrow channel in the middle area. The detailed analysis show the relationship of the transmission with the channel width, the width and energy of package. Obviously, the transmission of the wave packet increases with the increase of channel width and the package energy. For the wave packet with small package width the initial channel width does not vary with the energy. But for the large package width the initial channel width decreases with increasing energy. And the transmission of the wave packet decreases with the increase of channel length.
Related Dissertations
Last updated
Sponsored Links
Home |About Us| Contact Us| Feedback| Privacy | copyright | Back to top