Problem Set 10
Note:
This problem set is due Nov 22 before midnight.
Please leave it in my mailbox
located at the first floor of Rutherford building.
1.
Imagine I form a wavepacket for a free particle of mass
m
using only three plane waves of
momenta
k
0
,
k
0

Δ
k
2
and
k
0
+
Δ
k
2
with amplitudes proportional to 1
,
1
2
and
1
2
respectively.
Find the form of the wavepacket at time
t
= 0. Using a reasonable defination of Δ
x
, show
that
Δ
x
Δ
k
≥
4
π.
(1)
Find also the time evolution of the system and determine the peak of the wavepacket at a
time
t
. How will the result change if the three waves were electromagnetic?
2.
A neutron is emitted from a furnace at a temperature 300
K
. What is the deBroglie
wavelength of the neutron?
If I want the same wavelength for an electron, how much
potential difference (in volts) should I accelerate the electron through?
You will find
that for smaller wavelengths, we require higher energies. Therefore in some regime non
relativistic analysis can no longer hold. Can you calculate the deBroglie wavelength of an
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '05
 KeshavDasgupta
 mechanics, Mass, bound state

Click to edit the document details