17 The Route to Equilibrium

Abstract

The method we are going to present here also relies, like the approach based on Fermi’s Golden Rule, on a step-wise solution of the Schrödinger equation, but now taking superpositions of energy eigenstates as initial states into account. Naturally, this approach, like all other approaches, relies on approximations. The crucial approximation here is the replacement of some specific quantities by their Hilbert space averages. For almost all states the Hilbert space average will be a good approximation, if and only if the Hilbert space landscape is almost flat. Therefore, the approximation is supported by showing that it is indeed possible to assume such a flat Hilbert space. Finally, it will be possible to derive a rate equation, which describes the decay qualitatively.