AN ALGORITHM TO STUDY TUNNELLING IN A WIDE CLASS OF ONE-DIMENSIONAL MULTIWELL POTENTIALS .1.

We prove a theorem which gives an algorithmic solution to the problem of finding the logarithmic derivative of the ground state wave function of one dimensional systems. By means of this quantity, as it is well known, one can determine the lowest part of the spectrum of the Hamiltonian by probabilistic methods. We show that, in some natural classes of potentials, the complexity of our algorithm is less than $N^3$, where $N$ is the number of the absolute minima of the potential. Our approach allows a systematic treatment of cases of much higher complexity than those analyzed so far in the literature and it can be useful in the study of physical systems like, for example, long molecular chains or superlattice structures.