COMPARISON OF DECREASING EIGENFUNCTIONS F OR DIRAC AND KLEIN-GORDON OPERATORS - APPLICATION TO THE TUNNEL EFFECT

Motivated by questions posed by R. Carmona in [2], we study the decays of the eigenfunctions of the Klein-Gordon and Dirac operators: K = Op (w)h(square-root 1 + xi2 + V(x)), [GRAPHICS] These operators descibe p articules in restricted relativity, of spin 0 for the Klein-Gordon and of spin 1/2 for the Dirac operator, so it is natural to compare the r esults. When the variation of the potential is small, as in the nonrel ativistic limit, we show that the results are compatibles. On the othe r hand, we will see that there are cases, typically when the potential varies more than the energy of the mass of the particle, where the de cays are different. We give two examples where the tunneling effect al lows one to distinguish these two operators, one relative to the semi- classical limit, the other to the tight-binding approximation.