How can you derive the effective mass?

[bluejay27]

I have seen that the energy of the band structure is defined in the following form. How do you obtain this form of the equation? Additionally, how can you obtain the effect mass of the electron? Do you just manipulate algebraically the equation of the energy of the band structure and solve it for for the m_e*?

 

[M Quack]

Yes, pretty much, but only close to the minimum (electron) or maximum (hole) of the band.

https://en.wikipedia.org/wiki/Effective_mass_(solid-state_physics)

 

[bluejay27]

Yes, pretty much, but only close to the minimum (electron) or maximum (hole) of the band.

https://en.wikipedia.org/wiki/Effective_mass_(solid-state_physics)

Colorado School of mines have a comprehensive lecture in solid state physics. And describes this derivation of the effective mass using Newton's second law. http://solidstate.mines.edu/videonotes/VN_10_2.pdf
However, I was not able to find the first equation in this paper.

 

[M Quack]

In classical physics, kinetic energy is 1/2 mv^2 or p^2/2m.
In QM the momentum p=hbar k...