Transient adaptation of electrons to Bloch environments

The adaptation process of an electron created in a periodic structure is calculated both analytically and numerically. The electron in the form of a "free" wave packet is introduced into a periodic potential. The time-dependent Schrödinger equation is solved to obtain its quantum mechanical transient behavior. The results show that within the bands the electron's behavior, its velocity and acceleration, passes quickly (within ∼10fs) and in an oscillatory manner from the "free" to the "Bloch-like" types. The importance of the "worm-like" movement of the electron is manifested, and the validity of the analytical approximation is verified not too close to the band edges. At the bottom of the first band and in the band gaps, lengthier and more complicated phenomena appear.