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:
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 Spring '03
 Nelson
 mechanics, Work, Trigraph, ψn, a− ψn

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