Quantum Mechanics A Paradigms Approach

We explore the energy eigenvalues and eigenstates of a periodic series of potential energy wells with the purpose of creating a rudimentary model of a solid. Our model uses an approximate approach that emphasizes the interaction between neighboring atoms. We learn how the eigenstates of the periodic potential can be constructed from the eigenstates of the single elements of the periodic potential. We also learn that the eigenstates of a solid are characterized by a wavelength, and that the energies of those eigenstates form bands centered near the atomic energy eigenvalues. We model electron motion in solids with the use of a wave packet, a superposition of delocalized Bloch states.