Note that a naïve perturbation theory around one of those two vacua alone (of the Minkowskian description) would never show this non-perturbative tunneling effect, dramatically changing the picture of the vacuum structure of this quantum mechanical system. In fact the naive perturbation theory has to be supplemented by boundary conditions, and these supply the nonperturbative effect, as is evident from the above explicit formula and analogous calculations for other potentials such as a cosine potential (cf. Mathieu function) or other periodic potentials (cf. e.g. Lamé function and spheroidal wave function) and irrespective of whether one uses the Schrödinger equation or the path integral.