Stability of localized quantum states on the top of a barrier and some of its consequences: the specific case of a symmetric double well potential

It is demonstrated that barriers, like potential wells, can support localised states. However, barrier-localized states are seen to be much more short-lived compared to states localised in potential wells. These features are revealed with reference to a symmetric double-well potential by using the exterior complex-scaled Fourier grid Hamiltonian method. Some implications of the results are pointed out.