Classical Hamiltonian description of a two-level quantum system: The quantum Zeno effect

摘要

We consider the simplest quantum system, namely the two-level system with real matrix elements, and exhibit its specific phase properties related to the complex Hamiltonian formalism provided by a simple canonical transformation between the Schroedinger equation and a classical dynamical system that actually describes the dynamics of a spin 1/2. In the case of the quantum Zeno effect, it yields the provocative theoretical suggestion and experimental prediction that an energy measurement should always yield the same energy value (which is either the upper or the lower energy level, depending on the value of the energy expectation value), contrary to the standard quantum rule stating that an energy measurement should share the probabilities between the two energy levels (except for the eigenstates). This makes a quasi-continuously observed two-level quantum system very similar to a classical system from the point of view of energy measurements. (C) 1998 Elsevier Science B.V. [References: 30]