- #1

Rzbs

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- TL;DR Summary
- 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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- Thread starter Rzbs
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- #1

Rzbs

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- TL;DR Summary
- 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?

- #2

Lord Jestocost

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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

Rzbs

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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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Lord Jestocost

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"

- #5

Rzbs

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

Thanks

- #6

Lord Jestocost

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- #7

Rzbs

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This is the thing I didn't consider and now help me to understand...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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