Quantum coherence and formation of quantized states in semiconductors

We investigate the formation process of eigenstates in electromagnetic fields. Electronic eigenfunctions in crystalline solids in the electromagnetic fields are localized wavepackets associated with the discrete energy levels. The properties of such states (e.g. Landau levels in magnetic fields and Stark-ladders in electric fields) have been well revealed. However, it is obscure how transformation from the extended Bloch functions to the localized states occurs. By using the path-integral theory, we describe the transformation process of wave functions into quantized eigenstates. It is shown that self-interference, which may be interpreted as an afterimage of electronic motion, plays an important role in the transformation.