Physics 463  Final Exam
:
This exam is to be turned in 24 hours after it is received. In solving the following problems you may use any notes,
homework sets, and/or solutions accumulated during the semester,
one
quantum mechanics textbook (including
all volumes of a multivolume set such as CohenTannoudji, et al.), and one mathematical reference.
Your score will be based upon your 5 highest scores to the following 6 problems.
1.
Use the variational method to estimate the groundstate energy of an electron con
f
ned to the region
x
∈
[0
,L
]
by an in
f
nite squarewell potential to which an electric
f
eld
E
=
E
0
ˆ
x
has been applied. Choose a family of
trial states that satisfy appropriate boundary conditions at the edges of the well.
2.
The wave function of a particle subjected to a spherically symmetric potential
V
(
r
)
is given by
ψ
(
~
r
)=(
x
+
y
+3
z
)
f
(
r
)
.
(a) Is
ψ
an eigenfunction of
L
2
?
If so, what is the eigenvalue? If not, what values can be obtained if
L
2
is
measured?
(b) If
L
z
is measured, what values can be obtained and with what probabilities?
(c) Suppose it is somehow known that
ψ
(
~
r
)
is an eigenstate of
H
. Indicate how one may determine
V
(
r
)
.
3.
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 Fall '10
 PaulE.
 mechanics, Atom, Work, Quantum Mechanics textbook, radial function ykl, dr2 r2, light spinless projectile

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