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Physics
Atomic and Condensed Matter
Understanding the Derivation of Effective Mass Approximation in Semiconductors
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[QUOTE="aaaa202, post: 5455513, member: 294903"] I have noticed that in a lot of theoretical modelling of semiconductors you assume that the electrons living in the bottom of the conduction band obey a free particle Hamiltonian: H = p^2/2m* , where m* is the effective mass in the conduction band and p^2 is the usual differential operator. I am not sure how this is derived rigourously. I suppose you solve the band structure and show that as a function of k the band structure is parabolic in k about the minimum of the conduction band: E ≈ E0 + ħ^2k^2/2m* But how do you rigorously go from this expression, which contains the wave numbers k = (kx,ky,kz) back to differential operators? I hope you understand my question. [/QUOTE]
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Atomic and Condensed Matter
Understanding the Derivation of Effective Mass Approximation in Semiconductors
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