This preview shows pages 1–2. Sign up to view the full content.
PHYS 115A Homework 4 Solutions Winter 2008
revisions added February 12:
see ADDITIONAL NOTE below and Problem 1
The message below was emailed to the class
before this homework assignment was due:
As noted at the beginning of class, the lecture notes are merely notes and should not be trusted as a
reference. You should always refer to the textbook when copying equations or results, especially for
homework or when studying for exams.
There are some errors in Notes 3 that might aﬀect people that ignore the advice above and instead
use the notes as a reference.
Please make the corrections in your copy of the notes:
Notes 3: Simple Quantum Systems, Section 9: The Harmonic Oscillator
•
Eq. 75: First line. There should be a negative sign in front of the second partial derivative term.
•
Eq. 82: 3rd line. The factor of
~
ω
0
at the beginning of the line should not be there.
•
Eq. 84: The positive sign should be a negative sign, otherwise if you solve for
E
n
you don’t get
the right eigenvalues for the SHO.
•
Eq. 85: Both negative signs should be positive signs, otherwise if you solve for
E
n
you don’t get
the right eigenvalues for the SHO.
•
Eq. 105:
n
should be (
n
+ 1)
•
Eq. 106: (
n
+ 1) should be
n
ADDITIONAL NOTE (added February 12):
There are many places in Notes 3 of the class reader, starting at equation (104), where Ψ
n
(
x,t
) should
be corrected to
ψ
n
(
x
). This is because when the operators
a
+
and
a

act on an energy eigenstate
Ψ
n
(
x,t
) =
ψ
n
(
x
)
e

iE
n
t/
~
, they only aﬀect the spatial wavefunction
ψ
n
(
x
), and they don’t change the
timedependent factor
e

iE
n
t/
~
.
For example, the following are correct:
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.
This note was uploaded on 03/01/2009 for the course PHYS 115A taught by Professor Nelson during the Spring '03 term at UCSB.
 Spring '03
 Nelson
 mechanics, Work

Click to edit the document details