PHYS 71
Quantum Mechanics
Fall 2002
Week #3: Wednesday, Oct 16 - Monday, Oct 21
Reading: GriÆths: Chapter 6
Homework #2: Due Monday, Oct 21 at 5 PM. (to Yong Zhang)
Before you do these problems, please do the \tune-up" problems from Chapter 6.
From Chapter 6 (don't hand in): 3, 5, 10, 13, 15, 19
If any of this material is incomprehensible, please see me as soon as possible.
Chapter 6 homework (hand in): Problem 3.50, 6.2, 6.5, 6.9, 6.13
Notes:
For Problem 3.50, please use the ladder operators for the harmonic oscillator using Dirac
notation and use our ladder operators from last week. The raising and lowering operators
are
a=
and
ay =
r m!
i
(
x+
p)
2h
m!
r m!
2h (x
i
p)
m!
From the commutation relation for x and p, you can show
1
y
H = h ! a a
2
The normalized eigenkets are labeled by n:
(x) = jni
The commutation relation for the raising and lowering operator:
[a; ay] = 1
What do these operators do?
p
p
ajni = njn 1i; ay jni = n + 1jn + 1i
From this you should be able to show that aya is the number operator:
ayajni = njni; N^ = ay a:
Review: What is expansion? This is expansion. You want a C.O.N. basis.
X
j i = j ih j i
n
i
i
i
It's ne if you want to use a computer to do the integrals.