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NON-STANDARD REPRESENTATIONS OF THE DIRAC EQUATION AND THE VARIATIONAL METHOD

  • MONIKA STANKE
  • JACEK KARWOWSKI
Conference paper
Part of the Progress in Theoretical Chemistry and Physics book series (PTCP, volume 15)

Abstract

An application of the Rayleigh-Ritz variational method to solving the Dirac-Coulomb equation, although resulted in many successful implementations, is far from being trivial and there are still many unresolved questions. Usually, the variational principle is applied to this equation in the standard, Dirac-Pauli, representation. All observables derived from the Dirac equation are invariant with respect to the choice of the representation (i.e. to a similarity transformation in the four-dimensional spinor space). However, in order to control the behavior of the variational energy, the trial functions are subjected to several conditions, as for example the kinetic balance condition. These conditions are usually representation-dependent. The aim of this work is an analysis of some consequences of this dependence.

Keywords

Variational Principle Dirac Equation Dirac Spinor Angular Momentum Quantum Number Energy Hypersurface 
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.

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Copyright information

© Springer 2006

Authors and Affiliations

  • MONIKA STANKE
    • 1
  • JACEK KARWOWSKI
    • 1
  1. 1.Instytut FizykiUniwersytet Mikołaja KopernikaToruńPoland

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