Transcript Introduction to Electromagnetism

Winter Physical Systems:
Quantum and Modern physics
Dr. E.J. Zita, The Evergreen State College, 6.Jan.03
Lab II Rm 2272, [email protected], 360-867-6853
Program syllabus, schedule, and details online at
http://academic.evergreen.edu/curricular/physys2002/home.htm
Monday: QM (and Modern Q/A)
Tuesday: DiffEq with Math Methods and Math Seminar
(workshop on WebX in CAL tomorrow at 5:00)
Wed: office hours 1:00
Thus: Modern (and QM Q/A) and Physics Seminar
TA?
Outline:
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Logistics
Modern physics applies Quantum mechanics
Compare Quantum to Classical
Schroedinger equation and Planck constant
Wave function and probability
Exercises in probability
Expectation values
Uncertainty principle
Applications… Sign up for your minilectures
Time budget
E&M
5 hrs class
4 hrs reading
6 hrs homework
DiffEq
5 hrs class
4 hrs reading
6 hrs homework
Mechanics
5 hrs class
4 hrs reading
6 hrs homework
Total time
15
12
18
46 minimum
Plus your presentations:
* minilectures (read Learning Through Discussion and ML Guidelines)
* library research (to prepare for projects in spring)
Science Seminar:
* Tues. Math seminar: Chaos and Humor
* Thus. Physics seminar: Alice and Heisenberg
Quantum Mechanics
Modern Physics
by Griffiths
by OHanian
Theory : careful math and
careful reasoning
Applications: more
numerical than theoretical
Links between QM and Modern
From Tom Moore’s Unit Q
How can we describe a system and
predict its evolution?
Classical mechanics:
Force completely describes a system:
Use F=ma = m dp/dt to find x(t) and v(t).
Quantum mechanics:
Wavefunction y completely
describes a QM system
Review of Modern physics basics
Energy and momentum of light:
E
hc

 pc
p
h

Can construct a differential operator for momentum
(more careful derivation in a few weeks)
h

2
k
2

h

2

p 
 k
 
x
2
h
Planck constant h = 6.63 x 10-34 J.s
Invented by Planck (1900) to phenomenologically
explain blackbody radiation
Planck derived h from first principles a few weeks later,
treating photons as quantized in a radiating cavity
Fundamental unit of quantization, angular momentum
units
Used by Einstein to explain photoelectric effect (1905)
and Bohr to derive H atom model (1912)
Schroedinger eqn. = Energy conservation
E=T+V
Ey = Ty + Vy
where y is the wavefunction and
energy operators depend on x, t, and momentum:

p̂  i
x
y
i

t

E i
t
y
 Vy
2
x
2
2
Solve the Schroedinger eqn. to find the wavefunction, and
you know *everything* possible about your QM system.
Wave function and probability
Probability that a measurement of the system will yield a
result between x1 and x2 is
x2
 y ( x, t )
x1
2
dx
Measurement collapses the wave function
•This does not mean that the system was at X before the
measurement - it is not meaningful to say it was localized at
all before the measurement.
•Immediately after the measurement, the system is still at X.
•Time-dependent Schroedinger eqn describes evolution of y
after a measurement.
Exercises in probability: qualitative
Exercises in probability: quantitative
1. Probability that an individual selected at random has age=15?
 j N ( j )   j P( j )
2. Most probably age? 3. Median?
j 

N
j 0
4. Average = expectation value of repeated measurements of
many identically prepared system:
 j N ( j )   j P( j )
j 
N
5. Average of squares of ages =

2
2
j 0
6. Standard deviation s will give us uncertainty principle...
Exercises in probability: uncertainty
Standard deviation s can be found from the deviation from the
average: j  j  j
But the average deviation vanishes:
j  0
So calculate the average of the square of the deviation:
s 2   j 
Homework (p.8): show that it is valid to calculate s more easily
by:
2
s 2  j2  j
1.1 Find these quantities for the exercise above.
2
Expectation values
Most likely outcome of a measurement of position, for a system
(or particle) in state y: 
x 
 x y ( x, t )
2
dx

Most likely outcome of a measurement of position, for a system
(or particle) in state y:
d x
p m
 i
dt

 * y
 y x

 dx

Uncertainty principle
Position is well-defined for a pulse with ill-defined
wavelength. Spread in position measurements = sx
Momentum is well-defined for a wave with precise . By its
nature, a wave is not localized in space. Spread in
momentum measurements = sp
We will show that
s xs p 
2
Particles and Waves
Light interferes and diffracts - but so do electrons! in Ni crystal
Electrons scatter like little billiard balls - but so does light! in
the photoelectric effect
Applications of Quantum mechanics
Blackbody radiation: resolve ultraviolet catastrophe, measure
star temperatures
Photoelectric effect: particle detectors and signal amplifiers
Bohr atom: predict and understand spectra and energies
Structure and behavior of solids, including semiconductors
Scanning tunneling microscope
Zeeman effect: measure magnetic fields of stars from light
Electron spin: Pauli exclusion principle
Lasers, NMR, nuclear and particle physics, and much more...
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