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 d
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 ) +
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
pho
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
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
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
pin
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, i
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
ex
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 poi
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 (
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.
Mark
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
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.
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
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
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 Hermitia
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)