ABSTRACT
In the framework of nonrelativistic quantum mechanics we derive a necessary condition for four Coulomb charges (m1(+), m2(-), m3(+), m4(-)), where all masses are assumed finite, to form the stable system. The obtained stability condition is physical and is expressed through the required minimal ratio of Jacobi masses. In particular, this provides the rigorous proof that hydrogen-antihydrogen and muonium-antimuonium molecules and hydrogen-positron-muon systems are unstable. It also proves that replacing hydrogen in the hydrogen-antihydrogen molecule with its heavier isotopes does not make the molecule stable. These are the first rigorous results on the instability of these systems.
ABSTRACT
In this paper we postulate and solve the following problem: Prove in the framework of Newtonian mechanics that three Coulomb charges (-1,Q,Q) for Q>4 will leave any initial volume in a finite time and estimate this time. We also discuss possible generalizations of the problem and its relation to stability of ions and molecules.
