Universitet Analytic structure of many - body Coulombic wave functions

We investigate the analytic structure of solutions of non-relativistic Schrödinger equations describing Coulombic manyparticle systems. We prove the following: Let ψ(x) with x = (x1, . . . , xN ) ∈ R denote an N -electron wavefunction of such a system with one nucleus fixed at the origin. Then in a neighbourhood of a coalescence point, for which x1 = 0 and the other electron coordinates do not coincide, and differ from 0, ψ can be represented locally as ψ(x) = ψ(x) + |x1|ψ(x) with ψ, ψ real analytic. A similar representation holds near two-electron coalescence points. The Kustaanheimo-Stiefel transform and analytic hypoellipticity play an essential role in the proof.