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- assumptions of semiclassical model of electron dynamics

Why do we exclude interband transitions in semiclassical model of electton dynamics? I mean why it is an assumption in this model?

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In summary: So in this model if the applied electric field wasn't small then it wouldn't be able to account for interband transitions?Yes, that is correct.

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- TL;DR Summary
- assumptions of semiclassical model of electron dynamics

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"The next important subject we address is electron dynamics in metals. Our consideration will be based on a semiclassical model. The term “semiclassical” comes from the fact that within this model the electronic structure is described quantum-mechanically but electron dynamics itself is considered in a classical way, i.e. using classical equations of motion. Within the semiclassical model we assume that we know the electronic structure of metal, which determines the energy band as a function of the wave vector. The aim of the model is to relate the band structure to the transport properties as a response to the applied electric field.

Given the functions ##E_n(k)## the semiclassical model associates with each electron a position, a wave vector and a band index ##n##. In the presence of applied fields the position, the wave vector, and the index are taken to evolve according to the following rules:

(1) The band index is a constant of the motion. The semiclassical model ignores the possibility of interband transitions. This implies that within this model it assumed that the applied electric field is small..."

https://unlcms.unl.edu/cas/physics/tsymbal/teaching/SSP-927/index.shtml (see lecture note 10. Electron Dynamics and Fermi Surfaces)

- #3

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Thanks but I can't understand why in this model we need to consider applied electric field small? I only know it must be small in comparison to amplitude of wave packet as shown in the following picture, but I don't know why (this picture is for showing wave vectors but it also shows amplitudes):

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"

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Can you please explain what happens in this model if the applied electric field wasn't small?

Thanks

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This is the thing I didn't consider and now help me to understand...Lord Jestocost said:The semiclassical model of the electron dynamics in crystals is based upon the assumption that the wave packet representing the electron is asuperposition of Bloch states from a single band

Thanks for your explanation.

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