Born-oppenheimer approximation for some singular systems

Abstract

In this thesis we try to solve the energy spectrum of heavy particles in three body singular system by using the Born-Oppenheimer approximation. Heavy particles are carrying attractive Dirac-Delta function potential so, when we solve this system we see that the energy spectrum of heavy particles goes like {u100000} m M 1 3 . It is di erent from the well-known articles. After this result we look at the three body system from the many body perspective and we verify that our previous results are true. Afterwards we expand many body equations until second order we nd second order energy correction to the original energy. This energy goes like {u100000} m M 2 3 and we see not only the second order of the potential term but the second order of the kinetic part also makes a contribution to the second order energy. We nd new results show that high order energy corrections can be calculated systematically. In