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

Abstract

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 forH _K (c)−mc ², 3) the nonrelativistic limit of the eigenvalues ofH _K (c)−mc ².