Boundary conditions for many-electron systems

Péter V. Tóth

Published 2010-10-13, updated 2011-06-02Version 4

It is shown that natural boundary conditions for non-relativistic wave functions are of periodic or of homogeneous Robin type. Using asymptotic central symmetry of Hamiltonian and theory of singular differential equations the many-electron wave function is expanded in series both in the vicinity of Coulomb singularities and at infinity. Hydrogenic angular dependence of three leading terms of expansion about Coulomb singularities is found. Exact first- and second-order cusp conditions are obtained demonstrating redundancy of spherical average in Kato's cusp condition. Our first-order cusp condition exhibits CP symmetry. Homogeneous Robin boundary conditions are obtained for aperiodic many-electron systems from the expansions. Use of our explicit boundary conditions improves both speed and accuracy of numerical calculations. A confluent hypergeometric series defining arbitrarily high order cusp conditions for the spherically averaged Hamiltonian is presented.