Ground state energy splitting in the Razavy potential in semi-classical approximations
Christopher Künster, Münster
I studied the quality of approximation methods developed specifically for double well potentials like the semiclassical pathintegral approach on the basis of the Razavy potential. This type of potential belongs to the so called quasi exactly solvable class which take up an intermediate role in between the vast majority of analytically insoluble potentials and the few which give rise to exact solutions. In the 1980s Razavy proposed this one dimensional effective potential as a first approximation to describe the energy levels of the ammonia system whose two lowest levels are used for the ammonia maser. In this picture the three hydrogen H span a plane to which the nitrogen N has the distance $x$. Due to electrostatic repulsion the nitrogen will omit the region in the plane between the hydrogen but on the other hand van der Waals forces will not let it escape too much, thus building the typical tetrahedron structure of the ammonia. The problem is symmetric with respect to the H-H-H plane which gives rise to the double well structure. As a consequence of this double well the energy gap is very small and does not allow conventional perturbation theory to be applied. I present the procedure which is basically a one loop calculation and compare th results to the exactly known solution.