Communications in Mathematical Physics

, Volume 94, Issue 4, pp 523–535 | Cite as

One electron molecules with relativistic kinetic energy: Properties of the discrete spectrum

  • Ingrid Daubechies


We discuss the discrete spectrum of the operator
$$H_K (c) = \left[ { - \hbar ^2 c^2 \Delta + m^2 c^4 } \right]^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} - \sum\limits_{k = 1}^K {Z_k e^2 \left| {x - R_k } \right|^{ - 1} } $$
. More specifically, we study 1) the behaviour of the eigenvalues when the internuclear distances contract, 2) the existence of ac-independent lower bound forHK(c)−mc2, 3) the nonrelativistic limit of the eigenvalues ofHK(c)−mc2.


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Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • Ingrid Daubechies
    • 1
  1. 1.Theoretische NatuurkundeVrije Universiteit BrusselBrusselBelgium

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