The projected single-particle Dirac operator for Coulombic potentials

  • D.H. Jakubassa-Amundsen

    Mathematics Institute University of Munich Theresienstr. 39 80333 Munich Germany
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Abstract

A sequence of unitary transformations is applied to the one-electron Dirac operator in an external Coulomb potential such that the resulting operator is of the form to any given order in the potential strength, where and project onto the positive and negative spectral subspaces of the free Dirac operator. To first order, coincides with the Brown-Ravenhall operator. Moreover, there exists a simple relation to the Dirac operator transformed with the help of the Foldy-Wouthuysen technique. By defining the transformation operators as integral operators in Fourier space it is shown that they are well-defined and that the resulting transformed operator is -form bounded. In the case of a modified Coulomb potential, one can even prove subordinacy of the -th order term in with respect to the st order term for all , as well as their -form boundedness with form bound less than one.

Cite this article

D.H. Jakubassa-Amundsen, The projected single-particle Dirac operator for Coulombic potentials. Doc. Math. 10 (2005), pp. 331–356

DOI 10.4171/DM/191