Hidden Optimal Principle in Quantum Mechanics and Quantum Chemistry

Quantum Mechanic axioms are the result of the microscopic cooperative equilibrium among symmetric players (quantum object and human subject). On the other hand, we introduce Nash’s equilibrium in Hilbert space, which has two characteristics: it is a fixed point and it maximizes a utility function. Moreover, evolution and selfadjoint operators have interesting properties which allow us to study steady state in Evolutionary Game Theory. Also, we present cooperative games in complex systems language.The concept of cooperation is important in game theory but is somewhat subtle. The term cooperate means to act together, with a common purpose. Incentive compatibility is equivalent to synergy principle, which appears naturally (to add or to multiply utilities, ec[34]). Finally, wein the relevant results not only proved the main theorems of Quantum Mechanics, Quantum Chemistry and its applications to salt-water but also we resolved some main questions such us: Do hydrogen-bonded networks, in which tunneling plays an important role, exist?, How cooperation and entropy affect water cluster equilibria?. Can salt (ClNa) play an Nobel role in photo-catalysis?. The answers are: tunnel effect it is possible in salt water but not in water, because ClNa, visible light or electricity incentive to produce catalysis or photo-catalysis. Also, If hydrogen-bonded networks and water cluster size increases complexity of an global equilibrium, then tunnel effect appears as an local equilibrium.