A simple way to obtain average occupation on quantum systems

Abstract In this work, we present a simple method to obtain time average occupation of quantum systems with time-independent Hamiltonian. Our method is fast and can be used for system with large Hilbert space. The average occupation can give insights and help finding the best parameter to be used in experiments or for a more complex simulation using time-depended Hamiltonian and density matrix. As an example of application, we use this method to find the best parameters to send a laser to excite a two-level system coupled to cavity mode to a final state.