Resonance transfer of molecular excitation energy

Abstract

The rate of energy transfer between two identical molecules in empty space is calculated, assuming that initially one molecule is excited and the other is in its ground state, and that electric dipole interactions are responsible for the coupling. The time-dependent Schrödinger equation for molecules and radiation is solved by Van Hove's resolvent operator. The probability that the second molecule is excited oscillates with time at close distances and decays exponentially at long distances. This calculation leads to the apparent contradiction that the excitation energy travels faster than light. The difficulty disappears if one looks at the behaviour of observables rather than wave functions. Calculations are made for the situation where the molecules start in their ground state and then the first one is excited by an external source of radiation. The dipole moment of the second behaves in almost the same way as if the two molecules were a pair of coupled damped harmonic oscillators.