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Physics 2D — Spring 2010
Quiz #6
Friday May 28
11:00am to 11:50am
[Note:
This is a closedbook exam.
No calculator is allowed.
The total score
of this exam is 50 points.
Points assigned to each problem is a guide to how
many minutes you should spend working on it.]
Possibly useful formulae:
•
k
= 2
π/λ
,
ω
= 2
πf
, ¯
h
=
h/
(2
π
)
•
de Broglie:
E
= ¯
hω
,
p
= ¯
hk
•
Heisenberg’s uncertaity principle: Δ
x
·
Δ
p
≥
¯
h/
2
•
timeindependent Schr¨
odinger’s equation for spherically symmetric potential in 3dimension:

¯
h
2
2
m
∇
2
ψ
+
U
(
r
)
ψ
(
r,θ,φ
) =
E ψ
(
r,θ,φ
)
•
diﬀerential equation for the radial wave function
R
(
r
) resulting from separation of variable:
ψ
(
r,θ,φ
) =
R
(
r
)
·
Y
(
θ,φ
)

¯
h
2
2
m
±
R
00
+
2
r
R
0
²
+
"
U
(
r
) +
‘
·
(
‘
+ 1)¯
h
2
2
mr
2
#
R
(
r
) =
E R
(
r
)
•
diﬀerential equation for the angular wave function
Y
(
θ,φ
) resulting from separation of vari
able:
ψ
(
r,θ,φ
) =
R
(
r
)
·
Y
(
θ,φ
)
"
∂
2
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 Spring '08
 Hirsch
 Physics, Work

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