Quantum Mechanics 215C Homework Solutions #1
April 14, 2004
1. (5 Points)
(a) The problem is completely done in the text, on pages 406-408.
2. (a) Given that:
b2 + z 2 dz
we substitute the gaussian potential V = V0 exp
Quantum Mechanics 215A Homework Solutions #8
November 24, 2003
Average score: 27.8/30. Common errors were forgetting that and are complex, and missing
a subtle sign issue in 2b.
1. Weve all done the rst part a ton of times now, Ill just quote
Quantum Mechanics 215A Homework Solutions #6
November 10, 2003
Average score: 14.1/15.
23. (7 Points) We know from the previous homework that the wavefunction at t < 0 is:
(x) = e|x|
where m/ 2 . To nd the time evolution of this wave fun
i f d b`Y
V T Q 4 2 6H G CA98 6 42
Jz = h (N+ N ) N = N+ + N
J = a a
[Jz , J ] =
([N+ , J ] [N , J ])
[N+ , J ] = [N+ , a a ] = [N+ , a ]a = a a
[N , a a ] = a [N , a ] = a a
[Jz , J ] =
Quantum Mechanics 215A Homework Solutions #4
October 26, 2003
Average score: 25.5/30.
1. (5 Points) First, a useful lemma: From the denition of the Heisenberg representation, AH (t) =
U (t)AU (t). Therefore:
[AH , B H ] = [U (t)AU (t), U (t)B
This is more or less a continuation of Ex-9
Using the eigenkets for the z,x,y referance frame.
a. The prepared beam can be represented by
b. The lter |a >< a | which will select a and reject a . Using Ex 9 the representation of this in z eige
Sakurai problem solutions (Chapter 1)
 Three SternGerlach lters are placed in series. The rst apparatus, oriented in the z direction, passes atoms having sz = + /2 and stops others. The
second apparatus is oriented at an angle to the z
Physics, 6th Ed.
Chapter 4. Translational Equilibrium and Friction
Chapter 4. Translational Equilibrium and Friction.
Note: For all of the problems at the end of this chapter, the rigid booms or struts are considered
to be of negligible weight. All forces