Quantum mechanics of two coupled H-bond protons: eigenstates, time evolution, spectral fluctuations, and chaos

Abstract

A system of two bilinearly coupled particles moving in two equal symmetric one dimensional double well potentials is considered. Varying the coupling strength changes the classical behaviour drastically. From a quantum mechanical treatment statistical properties of the spectrum (term spacing distributions, spectral rigidity) are derived and discussed in connection with the occurence of classical chaos. Furthermore, the time evolutions of wavepackets are discussed.