In pure metals with perfect periodicity, the Bloch wavefunction representing an electron, is delocalized throughout the crystal for all times and is an eigenstate of the one-electron Hamiltonian. Therefore, there is no change or "propagation" of this wavefunction in time. However, real conduction takes place in time.
How does one physically or mathematically understand the process of conduction dynamically i.e., in terms of a wavefunction which travels down the crystal from one lead of the battery to another lead connected across the sample in time?
I want to understand the process of conduction and for simplicity neglecting electron-electron interactions and all deviations from periodicities (such as ionic motion, defects, impurities etc).
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