Condensed Matter Physics - Nearly-Free Electron Approximation & Tight-Binding Approximation

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Kronig-Penney Model is an ideal model to deal with the motion of an electron inside a crystal,because the potential used in this model is not realistic. An exact description of the electronic behavior in a crystal must take into account the actual potential experienced by the electron due to the ion cores and all other electrons of the crystal. This is very complicated problem,so in practice two approximate methods are utilized,which are,Nearly Free Electron Approximation and the Tight Binding Approximation. When the periodic potential is very weak, we can treat it as a perturbation and we have the‘ nearly free electron approximation’. When the periodic potential is very strong,each electron is almost bound to a minimum in the potential and rest of the lattice is regarded as a perturbation on the above minimum,. This is known as the‘tight binding approximation’.