The Sojourn Time Of Inverted Harmonic Oscillator In Some Specific Magnetic Field

We study the influence of some specific magnetic field for the charge wave function.We start from Aharonov-Bohm effect and study the effect of flux quantum number on system evolution.We imagine a charged particle in a 2d inverted potential under a particular magnetic field.The influence of Aharonov-Bohm effect and the spin-orbit interaction was also considered.By using the path integral method,the evolution of wave function is obtained,and then the system sojourn time is calculated.In section one,we introduce the basic concepts of path integral,geometric phase and so on.In section two,the influence of tilted magnetic field on the sojourn time of charged particles in inverted potential is calculated by means of path integral method and giving the results of specific angles such as 0 degree and 90 degrees.In section three,we found that the effect of flux quantum number on sojourn time is not limited 0 to 1 as previously paper thought.Then,we studied the effect of spin-orbit interaction,and found that the spin-orbit coupling effect would cause the sojourn time curve to split.But,this effect is too weak to see in the experiment.