ABSTRACT
If the Hamiltonian is time-dependent, the solution of the time-dependent Schr dinger equation in general becomes difficult. Quantum zeno effect, named by Misra and Sudarshan, is an inhibition of induced or spontaneous transition between quantum states by frequent measurements, so that the system remains in its initial state throughout a long time interval. The frequent measurements decouple the interaction between the system and the environment, and suppress the evolution of quantum state. The phenomenon of Berry phase was first discovered by Pancharantnam in 1956, independently by Longuet-Higgins in 1958, and more generally by Berry in 1984. The Landau-Zener formulas is to calculate the transition probability from an instantaneous lower energy eigenstate at infinite past to an instantaneous upper energy eigenstate at infinite future.
