Appendix D
Solutions to Appendix C problems
Solution to Exercise C.1.
a) We obtain Eq. (C.2) by substituting f (x) = 1 into Eq. (C.1).
b) Make a replacement of the integration variable x a = t. Then dt = dx and
+
+
(C.1)
(x a)f (x)dx =
(t)f (t + a)dt =
University of Calgary
Physics 443: Quantum Mechanics I
Assignment #5
Due Date: Monday, 12:00 p.m. February 18, 2013
1.
Show that probability satisfies the continuity equation given by
t
( r ,t ) + J ( r, t ) = 0
where J ( r,t ) is the probability cur
University of Calgary
Physics 443: Quantum Mechanics I
Assignment #3
1.
Due Date: Friday, February 1, 2013
(a)
(b)
Suppose you drop a rock off a cliff of height h . As it falls, you snap a million
photographs, at random intervals. On each picture you meas
University of Calgary
Physics 443: Quantum Mechanics I
Assignment #4
1.
Due Date: Friday, February 8, 2013
Prove the following general commutator identities. You may assume that all of the
operators A , B , C , and D are linear.
(a)
A , B , C + B , C , A
University of Calgary
Physics 443: Quantum Mechanics I
Assignment #1
Due Date: Friday January 18, 2013
1. Consider a metal that is being welded.
(a) How hot is the metal when it radiates most strongly at 490 nm?
(b) Assuming that it radiates like a blackb
University of Calgary
Physics 443: Quantum Mechanics I
Assignment #2
1.
(a)
Due Date: Friday, January 25, 2013
The needle on a broken car speedometer is free to swing, and become perfectly off the
pins at either end, so that if you give it a flick it is e
University of Calgary
Physics 443: Quantum Mechanics I
Assignment #7
Due Date: Monday, 12:00 p.m. March 18, 2013
1.
Consider a beam of particles starting at x and moving in the positive x
direction, incident on a potential of the form (with 0 1 ).
0
V
V
University of Calgary
Physics 443: Quantum Mechanics I
Assignment #10
Due Date: Tuesday, 12:00 p.m. April 16, 2013
1.
(a)
Show that for the Harmonic Oscillator, the position squared operator can be
expressed in terms of the raising and lowering operators
University of Calgary
Physics 443: Quantum Mechanics I
Assignment #8
Due Date: Monday, 12:00 p.m. March 25, 2013
What, if anything, is the parity of the function f ( x) x( x 2 3ax 2a 2 ) about the point
x a ? Show how you came to your conclusion.
1.
2.
If
2013 Physics 443 Midterm Equation Sheet
An ( x) ann ( x)
i
2 2
x, t
x, t V x, t x, t H x, t
2
t
2m x
h / p h / mv
E h
x, t dx x, t dx
2
c
Prob( x1 , x2 ) x, t dx
x2
2
x1
x, t dx x, t dx 1
f ( x) * x f ( x) x dx
x * x x x dx x x dx
2
2
xrms
x 2 x
Physics 443
Quantum Mechnics I
N. Ahmadi
Office: SB525
Office Hours: 1:00-3:00 M or by appointment
Email: [email protected]
Course material is available on University of Calgary
Blackboard.
Marking
scheme
1. Assignments ( 10):
20%
2. Quizzes
15%
3.
University of Calgary
Physics 443: Quantum Mechanics I
Assignment #6
1.
Due Date: Monday, 12:00 p.m. March 4, 2013
Show that
x dp * ( p) i
p
( p)
Solution:
Start with the position space expression of the expectation value of position:
x * (x) x (x) dx
[1
University of Calgary
Winter semester 2007
PHYS 443: Quantum Mechanics I
Final examination
April 20, 2006, 12.0015.00 (3 hours)
Open books. Answer all questions. Calculators permitted but not needed.
Total points: 100.
Problem 1 (10 pts). A state of a spi
University of Calgary
Winter semester 2006
PHYS 443: Quantum Mechanics I
Final examination
April 20, 2006, 12.00-15.00 (3 hours)
Open books. Answer all questions. Calculators permitted but not needed
Total points: 100
Problem 1 (10 pts) A photon polarized
University of Calgary
Winter semester 2011
PHYS 443: Quantum Mechanics I
Final examination
April 27, 2011, 12:00-15:00 (3 hours)
Total points: 100. Open books. No communication equipment allowed. You must solve all
problems in order to receive full credit
Chapter 9
Solutions to chapter 4 problems
Solution to Exercise 4.7. For example, the x component of the angular momentum is dened
as Lx = y pz z py . The position and momentum observables are Hermitian; in addition, we have
[, pz ] = [, py ] = 0. We can t
Chapter 8
Solutions to chapter 3 problems
Solution to Exercise 3.1.
a) We calculate the right-hand side of Eq. (3.5) using the decomposition (3.3) (we call the integration variable x ):
x| =
+
(3.1)
(x ) x| x dx =
+
(x ) (x x )dx = (x).
(8.1)
The last e
A Free Particle in one dimension
A free particle, as the name implies, is free of external forces or fields. A
free particle is an idealization, no system is truly isolated from external
influences.
However, in many situations the external forces that do