Band structure Kronig-Penney

Band Theory of Metals, Three approaches predict the electronic band structure of metals. The first approach (Kronig-Penney), the periodic potential method, starts with free electrons and then considers nearly bound electrons. The second (Ziman) takes into account Bragg reflection as a strong disturbance in the propagation of electrons. The third approach (Feynman) starts with completely bound electrons to atoms and then considers a linear combination of atomic orbitals (LCAOs). 

The Kronig-Penney band structure can range from free-electron-like behaviour to free-atom-like behaviour by changing the strength of the barrier, . It follows from eqn (5.26) that as i -+ 0, cos Ka - cos ka, and hence... 

The influence of the periodic potential of the crystal lattice on the electronic structure is introduced through the one-dimensional Kronig-Penney model that illustrates the essential features of band theory of solids. 

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