A new proof of the propagation theorem forN-body quantum systems

Gian Michele Graf

Erik Skibsted

John Michael Graf

Hideo Tamura

Kheir-Eddine Boudjemaa, Sami R. Zouzou

We begin by deriving explicit formulae for the energy levels of a system of N harmonic oscillators for two special mass configurations but for arbitrary N . Under the same conditions, we can perform analytically all the calculational procedure leading to an optimized lower bound for the ground state energy of an N -body system. The lower bound obtained in this way proves to be identical to the exact result. It is the first time, to our knowledge, that an explicit analytical proof of saturability has been worked out.

Israel Michael Sigal, Jingxuan Zhang