Bohmʹs particle on an interatomic surface: a brief note

In preceding work (Phys. Lett. A 286 (2001) 61; Europhys. Lett. 57 (2002) 20) we investigated the statistical meaning of Baderʹs interatomic surface under different Thomas–Fermi levels of approximation. In particular within Thomas–Fermi–Dirac–Weizsacker model we showed that at an interatomic surface, as defined by Bader, the normal component of the gradient of electrostatic plus Bohmʹs potential is equal to zero (Eur. Phys. Lett. 57 (2002) 20). In this communication we show the consequences of this result in terms of single quantum particle trajectory. The results show that Baderʹs surface is a surface of statistical equilibrium. Although in our preceding work we have already shown that the interatomic surface expresses equilibrium between statistical subsystems, the procedure adopted here considers electrons as explicit quantum particles with associated wavefunction, thus directly connects the quantum nature of the single particle with the statistical properties of the whole system. This picture is indeed very interesting since provide, within the framework of Baderʹs theory, an intriguing link between the quantum behavior of single particles, the statistical properties of the system they belong to and the chemical idea of atoms