Stability of matter

Basing on quantum mechanics and the simple Hamiltonian consisting of kinetic energy and Coulomb potential, heuristic arguments and estimates are used to guess the essential stability properties of many-particle systems. In view of applications in astrophysics, gravitation as a second potential and thermodynamic arguments are added. The guesses thus obtained are confronted with known exact results. The connection between the stabilities against explosion and against implosion, and thermodynamic stability is considered. In systems with a particle number larger than approx= 1054 (corresponding to the Jupiter mass) gravitational energy prevails over the electrostatic energy and determines the history of a star. Negative specific heat accompanies life and death of a star. Finally the role of stability and instability in the universe for life is outlined. (G.Q.)