However, if the variation is cyclical, the Berry phase cannot be cancelled; it is invariant and becomes an observable property of the system. By reviewing the proof of the adiabatic theorem given by Max Born and Vladimir Fock, in Zeitschrift für Physik 51, 165 (1928), we could characterize the whole change of the adiabatic process into a phase term. Under the adiabatic approximation, the coefficient of the n -th eigenstate under adiabatic process is given by C n ( t ) = C n ( 0 ) exp ⁡ ⁡ [ − − ∫ ∫ 0 t ⟨ ⟨ ψ ψ n ( t ′ ) | ψ ψ ˙ ˙ n ( t ′ ) ⟩ ⟩ d t ′ ] = C n ( 0 ) e i γ γ n ( t ) , where γ γ n ( t ) is the Berry's phase with respect to parameter t. Changing the variable t into generalized parameters, we could rewrite the Berry's phase into γ γ n [ C ] = i ∮ ∮ C ⟨ ⟨ n , t | ( ∇ ∇ R | n , t ⟩ ⟩ ) d R , where R parametrizes the cyclic adiabatic process. Note that the normalization of | n , t ⟩ ⟩ implies that the integrand is imaginary, so that γ γ n [ C ] is real. It follows a closed path C in the appropriate parameter space. Geometric phase along the closed path C can also be calculated by integrating the Berry curvature over surface enclosed by C .