Centre-of-Mass Separation in Quantum Mechanics: Implications for the Many-Body Treatment in Quantum Chemistry and Solid State Physics

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. We show 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 fully account for the COM problem. The Born-Oppenheimer (B-O) approximation reveals a secret: it is the limiting case where the degrees of freedom can be treated classically. Beyond the B-O approximation they are in principle inseparable. The (unique) covariant description of all the equations, with respect to the individual degrees of freedom, leads to new types of interactions: in addition to the known vibronic (electron-phonon) ones the rotonic (electron-roton) and translonic (electron-translon) interactions arise. We have proved that as a result of the COM problem only the hypervibrations (hyperphonons, i.e. phonons + rotons + translons) have a general physical meaning in molecules and crystals; nevertheless, the use of pure vibrations (phonons) is a justified procedure only for so-called adiabatic systems. This state of affairs calls for a total revision of our contemporary view of general non-adiabatic effects, especially in connection with the Jahn-Teller effect and in formulating better approaches to superconductivity. Although the vibronic coupling is primarily responsible for the removal of the electron (quasi-) degeneracies the explanation of symmetry breaking and the formation of molecular and crystallic structures, rotonic and translonic couplings are necessary.