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NNSE 618
Home assignment # 1
Due:
September 20, 2011
1. What is the de Broglie wavelength of a particle with energy 0.1 eV in vacuum with
effective mass of 10
31
kg? (2 points)
2. How will the energy of the lowest energy state in an infinitely deep potential well
change if the width of the potential well is doubled? (2 points)
3.
How do you reconcile the expression for the wave function of a free electron in space
(
x
,
y
,
z
,
t
)
A
exp[
i
(
k
x
x
k
y
y
k
z
z
)]exp(
i
t
)
with the Uncertainty Principle? (2 points)
4.
Find the magnitude of the wave vector of a free electron which has the same energy as
a photon with the wavelength of 0.55 μm.
Compare it with the magnitude of the wave
vector for this photon.
(2 points)
5. Assuming kconservation, calculate (in nm
1
) the phonon wavevector which can take an electron
from
valley to Lvalley in GaAs. (2 points)
6. Using tightbinding model calculate dispersion E(k) in the first Brillouin zone along one of the
major symmetrical axes <100> and effective mass (in the units of free electron mass, m
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This note was uploaded on 11/07/2011 for the course NNSE 618 taught by Professor Sergeoktyabrsky during the Spring '11 term at SUNY Albany.
 Spring '11
 SergeOktyabrsky

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