Centre-of-mass separation in quantum mechanics: Implications for the many-body treatment in quantum chemistry and solid state physics

TL;DR

This paper explores how center-of-mass separation impacts the understanding of many-body quantum problems in chemistry and physics, revealing new interactions and challenging traditional approximations like Born-Oppenheimer.

Contribution

It introduces a covariant framework that uncovers new types of interactions and emphasizes the importance of hypervibrations in non-adiabatic effects, calling for a revision of current theories.

Findings

Hypervibrations are physically fundamental in molecules and crystals.

Pure vibrations are only justified in adiabatic systems.

New interactions (rotonic and translonic) are essential for symmetry breaking.

Abstract

We address the question to what extent the centre-of-mass (COM) separation can change our view of the many-body problem in quantum chemistry and solid state physics. It was shown that the many-body treatment based on the electron-vibrational Hamiltonian is fundamentally inconsistent with the Born-Handy ansatz so that such a treatment can never respect the COM problem. Born-Oppenheimer (B-O) approximation reveals some secret: it is a limit case where the degrees of freedom can be treated in a classical way. Beyond the B-O approximation they are inseparable in principle. The unique covariant description of all equations with respect to individual degrees of freedom leads to new types of interaction: besides the known vibronic (electron-phonon) one the rotonic (electron-roton) and translonic (electron-translon) interactions arise. We have proved that due to the COM problem only the hypervibrations (hyperphonons, i.e. phonons + rotons + translons) have true physical meaning in molecules and crystals; nevertheless, the use of pure vibrations (phonons) is justified only in the adiabatic systems. This fact calls for the total revision of our contemporary knowledge of all non-adiabatic effects, especially the Jahn-Teller effect and superconductivity. The vibronic coupling is responsible only for removing of electron (quasi)degeneracies but for the explanation of symmetry breaking and forming of structure the rotonic and translonic coupling is necessary.