Stability of few-charge systems in quantum mechanics

Abstract

We consider non-relativistic systems in quantum mechanics interacting through the Coulomb potential, and discuss the existence of bound states which are stable against spontaneous dissociation into smaller atoms or ions. We review the studies that have been made of specific mass configurations and also the properties of the domain of stability in the space of masses or inverse masses. These rigorous results are supplemented by numerical investigations using accurate variational methods. A section is devoted to systems of three arbitrary charges and another to molecules in a world with two space-dimensions.

A short review about some exotic systems containing electrons, muons, and tauons

“…A review of some particular three unit charge systems along with the domain of stability of those systems has been presented, for example in Ref. [33].…”

“…However, despite the complexity of the calculations, enormous progress has been made (see for, example [33], for a review) in this field which has been rapidly developing ever since of the birth of non-relativistic quantum mechanics (Schrödinger equation). Moreover, one should note that the QED and relativistic corrections of the four-body systems of different flavors still remain a very challenging problem.…”

“…The theoretical investigation of the ''non-relativistic'' four-body systems interacting through Coulombic potential has been discussed in several works and some studies have been done regarding the existence of bound states of those systems and also the properties of the domain of stability in the space masses or inverse masses [33] (those results are supplemented by numerical investigations using accurate variational methods). The stability domain of the system made up of four particles of different masses, two having the same positive charge and two having the opposite negative charge, interacting only through Coulombic forces, can be represented in terms of points in the interior, or on the surface of a regular tetrahedron [32].…”

“…where two or three of the particles may have the same mass have been discussed in [31] (see also [33] for a review).…”

“…has been discussed by Richard [32] (see also [33]). The prediction of the stability of Coulombic few-body systems requires sophisticated calculations [34].…”