Numeric Research On The Critical Temperature Of Bose-Einstein Condensation

Bose-Einstein Condensation (BEC) is a subject on fire for scientific research. From its being brought forth in 1924 on, it kept the center attracting much of the studying interesting. And the researchers acquire great progress in the knowledge to this field, during the history of more than 70 years. In this period, achievements boomed both in the theoretical research and practical work, all the achievements being the condensation of intelligence and sweat of the researchers. Together with the development of technology needed in the experiment. Today study on BEC is going to reach the practical use - atomic laser. So it is still the frontier of scientific research.But the research hasn't reached the extent meaning what is called perfect. Many models and methods come out in a competitive way. We mean to make some study on the critical temperature of the Bose-Einstein condensation by a numeric method, using those firm backup the computer provides. We hope we can dig out more details of BEC 's character.Chapter I is the preface of this thesis. In this part we just tell the history of the Bose-Einstein condensation, covering the birth of this theory, the exploration in experiments proving the foresee of this theory , progress made in the understanding of the phenomenon , theoretical models for solving it, improvements in the technology and as a result the final implementation in the laboratory... Bose-Einstein Condensation, although more than 70 years old, is bringing to the science fresh air.Chapter II gives the relation between the critical temperature and the particle number through a direct numeric summary. BEC occurs at a extremely low temperature, at which the quantum effect proves to be quite outstanding. Generally, the Bose statistical formula will be transformed into integral manner to get the relation between the critical temperature and the particle population in an analytical form. But in the course of calculation, we must change the parameter to another so that our deduction can answer the continuum of the parameter. And this leads to the rub that we can't be sure of the accuracy of our method at low temperature. Numeric method can avoid such trouble for the sake of the quantum effect. And the results of these two methods really show difference. We analyze the condition for the condensation using the concept of entropy and reach the conclusion that there will be no BEC in the low dimension system. We get the relation between the critical temperature and the given number of the particles in a three-dimension infinite trap system directly, together with the tendency shown at a low temperature of the critical temperature' changing to the particle number. And point out the cause for the difference between the numeric method with the custom method by comparing these two methods. Also did we study the station of the harmonic potential trap in the same way. The difference at low temperature and the concordance at high temperature still appear. Analysis is made and all the results are shown in the form of graph. The result shows the tendency of the critical temperature's changing to the given particle number, when the quantum effect is major, is more slow than that got by the integral method. At last the affection of the chemical potential are taken into account to make it clear that the chemical must be involved in when we cope with BEC problem.Chapter III mainly disposes of the problem in the harmonic potential trap with interacting force. When interacting potential exists, the Hamiltonian embraces part having something to do with the wave function.So the schordinger equation became a nonlinear differential one which is beyond any analytical result. And we turn to numeric method in this chapter. By the demand of the wave function, such as normalization and finiteness, we solve the nonlinear equation. The energy levels were got and as a result the distribution of the states was also got. And thus we attain the changing tendency of the energy level under the condition of repulsive potential...