Deterministic quantum mechanics: The role of the Maxwell–Boltzmann distribution

Abstract

To be accepted by the community, the claim that nuclear motion has to be treated classically must be tested for all kinds of phenomena. For the moment we claim that in a quantum chemical calculation, a classical description of nuclear motion is superior to the use of the Schrödinger equation, and investigate how far we get with this statement. In the present paper we address the question what nuclear quantum statistics means in this context. We will show that the Maxwell–Boltzmann velocity distribution evolves quickly in any molecular dynamics simulation and this guarantees the physically correct behavior of molecular systems. Using first-principles molecular dynamics simulations, or more precisely Car–Parrinello molecular dynamics, we investigate what this means for Bose-Einstein condensates and for Cooper pairs. It turns out that our approach can explain all relevant phenomena. As a consequence, we can introduce a deterministic formulation of quantum mechanics and can get rid of all the paradoxa in traditional quantum mechanics. The basic idea is to treat electrons and nuclei differently.