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arXiv · 1405.4656

A variational approach to the Brown-Ravenhall operator for the relativistic one-electron atoms

Vittorio Coti Zelati·Margherita Nolasco
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Abstract

We use the Foldy--Wouthuysen (unitary) transformation to give an alternative characterization of the eigenvalues and eigenfunctions for the Brown-Ravenhall operator (the projected Dirac operator) in the case of a one-electron atom. In particular we transform the eigenvalues problem into an elliptic problem in the 4-dim half space $\mathbb{R}^4_{+}$ with Neumann boundary condition.

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Vittorio Coti Zelati, Margherita Nolasco. 2014-05-19. A variational approach to the Brown-Ravenhall operator for the relativistic one-electron atoms. https://doi.org/10.1016/j.na.2016.02.011

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