Physics 2D — Spring 2010
Quiz #3: Matter Waves
Friday April 30
11:00am to 11:50am
[Note:
This is a closedbook exam.
Only the use of 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:
•
Binomial expansion: (1 +
x
)
n
= 1 +
n
·
x
+
n
(
n

1)
2
x
2
+
...
•
k
= 2
π/λ
,
ω
= 2
πf
, ¯
h
=
h/
(2
π
)
•
de Broglie:
E
= ¯
hω
,
p
= ¯
hk
•
phase velocity:
v
p
=
ω/k
•
group velocity:
v
g
=
dω
dk
•
Heisenberg’s uncertaity principle: Δ
x
·
Δ
p
≥
¯
h/
2
•
Schr¨
odinger’s equation:
i
¯
h
∂
∂t
Ψ =

¯
h
2
2
m
∂
2
∂x
2
Ψ +
U
(
x
)Ψ
1
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
1.
Short answers: [10/50 points total]
(a)
Explain how Newton’s second law is incompatible with Heisenberg’s uncertainty principle.
Qualitatively, why is the uncertainty principle not important for macroscopic objects.
[5 points]
(b)
State Born’s interpretation of the wave function Ψ(
x, t
). Write down the normalization
condition at a particular time
t
, and explain what the condition means. Why can’t the
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '08
 Hirsch
 Physics, Mass, Uncertainty Principle, Fundamental physics concepts, group velocity, phase velocity

Click to edit the document details