ECE 306
Final Examination
Spring 2005
(3:00 to 5:00 PM, May 13, 2005. Open book and open notes.)
1.
Consider the wave function:
⎩
⎨
⎧
+
>
−
<
+
<
<
−
⎪
⎩
⎪
⎨
⎧
⎟
⎠
⎞
⎜
⎝
⎛
=
−
2
/
;
2
/
2
/
2
/
0
2
sin
)
,
(
/
a
x
a
x
a
x
a
for
e
a
x
A
t
x
h
iEt
π
ψ
(a)
Normalize this wave function (i.e. find A) and plot the space dependence of this
wave function.
(b)
Verify that the above wave function is a solution to the Schroedinger equation in
the region –a/2 < x < +a/2 for a particle which moves freely through the region
but which is strictly confined to this region that is bounded by two impenetrable
walls at x = ±a/2.
(c)
Determine the value of the total energy E of this state of the particle in the box
defined between the two walls at x = ±a/2. Is this state the ground state of the
particle in the box? Give the ground state energy of the particle in this box.
(d)
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 Spring '05
 TANG
 wave function, Eqs, 12 erg

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