An electron is confined to a plane. Within the plane it moves freely,
except the motion is restricted to an area of 
. A magnetic field B is
applied perpendicular to the plane.
(a) Calculate the energy levels.
(b) Calculate the degeneracy of each energy level.
(c) Assume that we have N = nA electrons and that the interaction between
the electrons is neglected.
Calculate and plot the magnetic field dependence of
the chemical potential 
for temperatures 
,
where 
is the cyclotron frequency.
(The peculiar behavior of this system is related to the integer quantum Hall effect
as discussed by Ibach and Lüth [4] p. 322.)
(d) Electrons of density 
cm 
are confined into a
100 Åthick layer. What is the typical magnetic field required to see
the effect discussed above? What temperatures are low enough at this field?
Laszlo Mihaly
Thu Oct 31 13:23:11 EST 1996
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