Abstract: The quantum traditional adiabatic theorem was present and traditional approximation conditions were given. Based on existence of insufficence about quntum traditional adiabatic approximation condition ,the new adiabatic theory and new adiabatic approximation condition were proposed and discussed by means of perturbative approach and a -invariant expasion. And finally,we make a deep analysis and discussion on the properties of quantum geometric potential contained in the new adiabatic condition..

Key words: quantum physics, quantum adiabatic theorem, adiabatic approximation conditions, invariant adiabatic orbit, quantum geometric potential