PH300 Modern Physics SP11
Charles Baily
Quantum Mechanics is the greatest intellectual accomplishment
of the human race. - Carl Wieman, Nobel Laureate in Physics, 2001
1/13 Day 1:
Why are we here…?
What do we need to do ?
Review some math…
What’s this class about ?
How do we plan on doing it ?
1
Today
• Introduction
• Why the class is as it is
• Structure of the class
• Lots of information…
• Posted on the Web:
(contact info, syllabus, course calendar and
deadlines, pre/post-class lecture notes, etc…)
http://tinyurl.com/PH300SP11
2
PH300 Course Information
Lecture: TR 9:30 – 10:45am Room: MH220
Instructor: Charles Baily
baily@colorado.edu
Office Hours: By appointment
Problem-Solving Sessions: Tuesdays 12:00 – 2:00pm (tentative)
Physics Library – MH325
Homework Due: Thursdays, beginning of class.
Course Website: http://tinyurl.com/PH300SP11
Textbook: Thornton & Rex, Modern Physics, 3rd edition (2006)
Some additional outside readings (available online)
3
Grading
• In-class & online participation (10%)
– Participation only
• Daily clicker participation, some in-class activities.
(2 “free” days credit)
– Graded
• Reading quizzes, occasional graded clicker question
• Homework (40%) (most of learning, collaboration helps)
– Weekly online (numeric/multiple-choice) and written homework.
– Weekly feedback, worth one point of homework extra credit.
one free week HW credit
Note: Total in-class and weekly homework is a MAJOR part of grade
Grade depends on showing up for class and doing homework.
• Exams (50%)
– (30%) Three midterm exams: In-class, dates 2/8, 3/29, 4/26
1 midterm grade dropped if all
– (20%) Final, date TBA
3 exams attempted
4
Put your name and contact
information on your clicker!
Power Indicator (lighted when on)
Low Battery Indicator (<10 h left)
replace 3 AAA batteries before next class
Vote Status
Green on for 0.5 sec indicates vote received
Flashing Red – not received
On-Off Button (keep on during class)
5
Set up your clicker
•
•
•
•
•
Everyday: swap clicker code to XX
Wait for 1st clicker question to open
Hold down On/Off Switch 4 seconds
Flashing blue light: enter X X
Type in Answer.
you’re set for rest of class period
• DO NOT TURN OFF CLICKER FOR CLASS (o.w.
repeat above for any new clicker question)
6
Have you used clickers
in a prior class?
• A –
• B –
Yes
No
You are NOT locked in to your first choice.
Final answer entered will be
the one recorded.
7
Why are you in this class?
8
What will be covered in PH300?
Special Relativity:
What happens when things go really fast?
Quantum Mechanics:
What happens when things get really small?
9
Topics in Special Relativity
• Classical physics before Einstein
• Simultaneity
• Time dilation and length contraction
• Geometry of “spacetime”
• Momentum, energy, and “E = mc2”
10
What is Quantum Mechanics?
Pre quantum-understood why stuff falls (gravity), a little about
properties of electric and magnetic fields, gases.
Quantum- understand underlying behavior of everything you
are likely to see or experience in your lifetime!
• properties of all basic materials
• properties of light and other EM radiation
• how light interacts with matter
• basis for all modern technology, etc.
11
PH300 Modern Physics – Spring 2011
Overall course goal:
Every student learn
everything!
12
PH300 Modern Physics – Spring 2011
General goals:
• Understand how modern physics has changed how we
view the world around us.
• Understand the microscopic origin of the behavior of
materials-- in the world and technological applications.
• Emphasis on understanding and applying concepts.
How do you know? Why does it matter?
• Some emphasis on interpretation
What does this all mean?
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2130 – 6 SEMESTERS
"I think quantum mechanics is an interesting subject."
1
0.9
AGREE
NEUTRAL
DISAGREE
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Pre-Instruction Average
(6 Semesters 2130)
Post-Instruction Average
(5 Semesters 2130)
Post-Instruction
2130FA10
Traditional Model of Education
Individual
Instruction via
transmission
Content (e.g. circuits)
15
Guiding principles: (basis for how course is run)
1. People understand concepts by seeing, discussing, and applying them, not by
passively listening to explanations.
2. Understanding physics (& solving problems that develop understanding)
is a learned skill, like golf or playing basketball or violin.
Takes time, effort, and practice. Research says better retention if sustained effort rather
than cramming.
3. People learn best by sharing and getting feedback on their thinking
-- Student-student more often than student-faculty.
4. Students learn most when they take the responsibility for what is learned.
Physics is not a collection of facts
It is way of thinking. Only you can teach yourself to think!
Analyzing, applying concepts, solving problems.
16
We provide you with opportunities to help you learn.
Content, problems, simulations, guidance, organization.
Learning only comes
as a result of your effort!
Model for learning in PH300
1. Read pre-class notes – introduce ideas and terms.
2. Analysis and discussion in class – explore, develop basic ideas and
understanding.
3. Master and retain ideas through use in extensive HW (4-6 hrs/wk)
(collaboration good, but submit own work)
17
Collective Work vs. Independent Work
Group Work Encouraged
(in fact, hopefully, necessary)
What is authorized:
- working with others to make sense of questions
- collectively sorting out the answer (explaining reasoning)
- writing up your own solution in your own words
What is NOT authorized:
- telling students the answer
- representing someone else’s work as your own
18
Problem Solving Sessions
Best education is one-on-one examination of thinking and
immediate feedback.
Learn to do for each other-- win-win situation, you both learn
more. Main learning time!
Location: Physics library – MH335
Regular Weekly Hours
(Starts next week)
Tuesdays: 12:00-2:00 pm
(subject to change; see course website)
19
20
What is your background in
mathematics?
My last completed mathematics course:
A)
B)
C)
D)
E)
2nd semester calculus
3rd semester calculus
Linear algebra
Differential equations
Higher math course…
21
Euler’s Equation
exp(i)  cos    i sin  
A) I know exactly what this equation means.
B) I think I know what this equation means.
C) I’ve seen it before but am not sure what it means.
D) I’ve never seen this equation before.
22
Some math to review
Comfort with algebra:
e.g.
Given at = b and cx + dt = f
and the values of a, b, c, d and f,
but you don't know the value of t or x,
solve for the value of x.
b
• solve for unknown t in terms of known quantities: t 
a
b
• put that into the other equation: cx  d  f
a
• Then solve for x:

1
b
f db
x  (f d ) 
c
a
c
c
a

23
Exponential notation
You should be comfortable with exp. notation
4 10
104
3
?
Note: e  exp( x)
x
e = 2.72
exp(0)  1
exp( x) exp( y )  exp( x  y )
exp( x)
 exp( x  y )
exp( y )
24
Basic calculus
Derivatives
dz
3
z = ax + bx + c, then
?
dx
d
cos( x)  ?
dx
d at
(e )  ?
dt
Integrals:
L
2
0

x
x
sin   cos   dx  ?
L
 L
Hint u = sin(x/L)
du = cos(x/l)1/Ldx
at
e
 dt  ?
25
Complex numbers
i  1
i2 = -1
z = x + i y (x is real part; y is imaginary part)
z* = x - i y complex conjugate; replace “i” with “-i”
Magnitude of z:
|z|2 = z*z
= (x - iy)(x + iy) = x2 + ixy – ixy + y2 = x2 + y2
Special result (from Taylor expansion):
ei = cos () + i sin()
26
Differential equations
What is the most general solution to the differential equation:
y ''( x)  k  y( x)
2
A)
B)
C)
D)
E)
y ( x)  A cos(kx)  B sin(kx)
y ( x)  A exp(ikx)  B exp(ikx)
y ( x)  A exp(kx)  B exp(kx)
A&B
A&B&C
27
Differential equations
y ''( x)  k  y( x)
d2
y ''( x)  2 cos  kx  
dx
d
  k  sin(kx)
dx
  k 2  cos(kx) =  k 2  y( x)
2
Function is
positive,
curvature is
negative
Function is
negative,
curvature is
positive
28
Differential equations
What is the most general solution to the differential equation:
y ''( x)  k  y( x)
2
A)
B)
C)
D)
E)
y ( x)  A cos(kx)  B sin(kx)
y ( x)  A exp(ikx)  B exp(ikx)
y ( x)  A exp(kx)  B exp(kx)
A&B
A&B&C
29
Differential equations
What is the most general solution to the differential equation:
y ''( x)  k  y( x)
2
exp(-kx)
Slope of function is always increasing (becoming less negative).
30