The E-k relation of a simple cubic lattice given by (4.79) is derived from the tight-binding approximation. Show that near k≈ 0 this relation can be expressed by =-ħ²/26₁a². Ek = Eno + where m* = n²/2ßna². And for kr /a, show that the E-k relation is given by ħ²k² 2m* where m* = ħ²k² 2m* Ek = Eno +
The E-k relation of a simple cubic lattice given by (4.79) is derived from the tight-binding approximation. Show that near k≈ 0 this relation can be expressed by =-ħ²/26₁a². Ek = Eno + where m* = n²/2ßna². And for kr /a, show that the E-k relation is given by ħ²k² 2m* where m* = ħ²k² 2m* Ek = Eno +
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Transcribed Image Text:The E-k relation of a simple cubic lattice given by (4.79) is derived from
the tight-binding approximation. Show that near k≈ 0 this relation can be
expressed by
:-ħ²/26₁a².
Ek = Eno +
where m* = n²/2ßna².
And for kπ/a, show that the E-k relation is given by
ħ²k²
2m*
where m* =
Ek
ħ²k²
2m*
= Eno +
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