Calculate the effective mass m* of electron with the momentum k- G/2 in a weak periodic potential U(r) = 2U0 cos(27x/a) for which the energy spectrum E(k) is given by Eq. (1.3.22) of Lect. 4. The mass m* is defined by the behavior of E(k) at k x G/2: h?q? E(k) = Em - G G 2m* Can m* be smaller or larger than the free electron mass?
Calculate the effective mass m* of electron with the momentum k- G/2 in a weak periodic potential U(r) = 2U0 cos(27x/a) for which the energy spectrum E(k) is given by Eq. (1.3.22) of Lect. 4. The mass m* is defined by the behavior of E(k) at k x G/2: h?q? E(k) = Em - G G 2m* Can m* be smaller or larger than the free electron mass?
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Transcribed Image Text:Calculate the effective mass m* of electron with the momentum
k G/2 in a weak periodic potential U(x) = 2Uo cos(27x/a) for which the
energy spectrum E(k) is given by Eq. (1.3.22) of Lect. 4. The mass m* is
defined by the behavior of E(k) at k G/2:
h?q?
G
G
k «
2
E(k) = Em
2m**
2
Can m* be smaller or larger than the free electron mass?
Transcribed Image Text:E2,1 (k) =
"
(Er + Ek-G) ± V(ER
(Ek- Ek-G)2 +U;
(1.3.22)
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The work done in where, v is the velocity and in the time.
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