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

  • Michal Svrček
Chapter
Part of the Progress in Theoretical Chemistry and Physics book series (PTCP, volume 22)

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.

Keywords

Adiabatic Approximation Adiabatic Limit Vibronic Coupling Degenerate Ground State Adiabatic Representation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

The author wishes to express his gratitude to E. Brändas for his valuable advice during compilation of this paper, to O. Šipr for critical reading of the manuscript and useful suggestions and to V. Žárský for constant help and encouragement.

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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • Michal Svrček
    • 1
  1. 1.Centre de Mechanique Ondulatoire AppliquéeCMOA Czech BranchCarlsbadCzech Republic

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