An algorithm to study tunnelling in a wide class of one-dimensional multiwell potentials. I

Abstract

The author proves a theorem which gives an algorithmic solution to the problem of finding the logarithmic derivative of the ground-state wavefunction of one-dimensional systems. By means of this quantity, as is well known, one can determine the lowest part of the spectrum of the Hamiltonian by probabilistic methods. The author shows that, in some natural classes of potentials, the complexity of the algorithm is less than N3, where N is the number of the absolute minima of the potential. The author's approach allows a systematic treatment of cases of much greater complexity than those analysed 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.