Unstable closed trajectories, librations and splitting of the lowest eigenvalues in quantum double well problem

We discuss the structure of asymptotic splitting formula for the lowest eigenvalues of multidimensional quantum double well problem. We show that the change of instanton by closed unstable trajectory of appropriate Hamiltonian system gives more natural and simpler preexponential factor (amplitude) in splitting formula. The projection of this trajectories onto configuration space are well know librations in classical mechanics.