Solution
Physics 214
Problem 5
Atom Recoil
Week 4
An atom can make a transition from a higher energy state to a lower energy state by emitting a
photon. To conserve momentum in the process, it must re
Solution
Physics 214
Problem 1
Phasor Addition
Week 2
We solved a problem similar to this last week. The idea here is to solve it using phasors.
To find the intensity due to more than one source, our
Physics 214
Waves and Quantum Physics
Lecture 1, p 1
Welcome to Physics 214
Faculty: Lectures A&B: Paul Kwiat
Discussion: Bryan Clark
Lecture C: Taylor Hughes
Labs: Tony Hegg
All course information is
Solution
Physics 214
Problem 3
Neutron 2-slit Interference Experiment
(two pages)
Week 4
In a 1991 article, R. Gahler and Z. Zeilinger describe a two-slit interference experiment done
with neutrons.
T
Physics214
Last Name:
Discussion Section:
Spring2016
MidtermExam
First Name
Discussion TA Name:
NetID
Instructions
Turn off your cell phone and put it away.
Keep your calculator on your own desk. Calc
University of Illinois
Spring 2015
ECE 310: Problem Set 4
Due: 6pm, February 20, 2015
Reading: 310 Course Notes Chapter 3.1, 3.2,
1. The sequence
( )
n , < n <
4
was obtained by sampling the continuo
Solution
Physics 214
Problem 2
Interference of three sources
Week 2
An audio oscillator drives three identical speakers, A, B, and C, that are at situated at the vertices
of an equilateral triangle. T
Physics 214.
Last Name:
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Midterm Exam
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Spring 2012
NetID
Instructions
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Keep your calculator on your own desk.
Solution
Physics 214 Useful definitions/identities: 1) z = a +bi = rei! , z ! a "bi = re"i# 2) z = z ! z
2
Problem 1 Complex Numbers and Phasors
Week 1
3) ec ! ed = ec+ d 4) ei! = cos! i sin ! e+i! +
Lecture7,slide24
18. An engineer wishes to propel a space-craft by firing a laser backward. The laser emits photons at
a rate of 1022 photons per second. Calculate the recoil force on the space-craft
1
University of Illinois
Spring 2015
ECE 310: Problem Set 1 SOLUTIONS
Due: 6pm, January 30, 2015
Reading: 310 Course Notes Chapter 1, Appendix A, Appendix D
1. Evaluate and represent your nal answer i
University of Illinois
Spring 2015
ECE 310: Problem Set 3
Due: 6pm, February 13, 2015
Reading: 310 Course Notes Chapter 2.5, 2.6
1. Evaluate the following expressions.
a) Find the inverse DFT of the s
University of Illinois
Spring 2015
ECE 310: Problem Set 1
Due: 6pm, January 30, 2015
Reading: 310 Course Notes Chapter 1, Appendix A, Appendix D
1. Evaluate and represent your nal answer in both Carte
Lecture1,slide30
Lecture2,slide16
2. Suppose that Speaker 1 is now pushed directly toward the listener by 1% of the wavelength of
the sound. How does the intensity at the listener change?
a. Decreases
Physics 214.
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Spring 2012
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Instructions
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Keep your calculator on your own desk.
Physics 214.
Midterm Exam
Fall 2012
The next two questions pertain to the following situation:
1. A laser light beam (the wavelength is 500 nm) hits a screen with three parallel slits with equal
spaci
Physics 214A
Midterm Exam
Spring 2014
Last Name:
Discussion Section:
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Instructions
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Physics 214*
Sample Final Exam
Spring 2010
Last Name:
First Name
ID
Discussion Section:
Discussion TA Name:
Exam Room & Building _ Seat Number_
Instructions Turn off your cell phone and put it away.
T
Physics 214*
Sample Final Exam
Spring 2010
Last Name:
First Name
ID
Discussion Section:
Discussion TA Name:
Exam Room & Building _ Seat Number_
Instructions Turn off your cell phone and put it away.
T
Lecture12:
Particlein1Dboxes,Simple
HarmonicOscillators
U(x)
(x)
U
n=2
n=0
U
n=1 n=3
x
Lecture 12, p 1
This week and last week are critical for the course:
Week 3, Lectures 7-9:
Light as Particles
Par
Physics 214*
Sample Final Exam
Spring 2010
Last Name:
First Name
ID
Discussion Section:
Discussion TA Name:
Exam Room & Building _ Seat Number_
Instructions Turn off your cell phone and put it away.
T
Lecture15:
TimeDependentQM&Tunneling
ReviewandExamples,AmmoniaMaser
U=
|(x,t=0)|2
U=
U(x)
0
U=
0
L x
|(x,t0)|2
U=
x
U0
E
0 L
x
L x
Lecture 15, p.1
Special(Optional)Lecture
Quantum Information
One of t
Lecture16:
3DPotentialsandtheHydrogenAtom
( x, y, z ) ( x) ( y ) ( z )
z
A real (2D) quantum dot
L
L
x
L
h2
http:/pages.unibas.ch/physmeso/Pictures/pictures.html
En x n y n z
n x 2 n y 2 n z 2
8mL2
Lecture18:
Orbitals,Spin,
andSelectionRules
z
Parametric Curve
1.2
1
x10( t )
0
x
y
1.2 1
1
1.2
0
y10( t )
1
1.2
Lecture 18, p 1
Special(Optional)Lecture
Quantum Information
One of the most modern app
Anyonewhocancontemplatequantum
mechanicswithoutgettingdizzyhasnt
understoodit.
NielsBohr
Lecture 17, p 1
Special(Optional)Lecture
Quantum Information
One of the most modern applications of QM
quantum
Lecture13:
BarrierPenetrationandTunneling
nucleus
x
U(x)
U(x)
U0
E
A B
0 L
x
0
C
B
A
x
Lecture 13, p 1
Today
Tunneling of quantum particles
Scanning Tunneling Microscope (STM)
Nuclear Decay
Solar F
Solution
Physics 214
Problem 5
Phased Array
Week 2
We can use interference effects to make a very directional antenna (either for transmitting or
receiving). As an example, consider the following situ
Physics214
Waves and Quantum Physics
Lecture 1, p 1
WelcometoPhysics214
Faculty: Lectures A&B: Paul Kwiat
Discussion: Bryan Clark
Lecture C: Taylor Hughes
Labs: Tony Hegg
All course information is on
Lecture19:
BuildingAtomsandMolecules
+e
r
n=3
n=2
n=1
+e
+e
r
even
Lecture 19, p 1
Today
Nuclear Magnetic Resonance
Using RF photons to drive transitions between nuclear spin
orientations in a magneti
UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN
Department of Electrical and Computer Engineering
ECE 310 Digital Signal Processing
Homework 4 Solution
Problem 1
Since = T and T =
1
1000
sec, the signal fr
Lecture 4:
Diffraction & Spectroscopy
y
d
L
Spectra of atoms reveal the
quantum nature of matter
Take a plastic grating from the bin as you enter class.
Todays Topics
Multiple-slit Interference*
Diffr
Quantum mechanics is the description of
the behavior of matter and light in all its
details and, in particular, of the happenings
on an atomic scale. Things on a very small
scale behave like nothing t
All of modern physics is governed by
that magnificent and thoroughly
confusing discipline called quantum
mechanics.It has survived all tests and
there is no reason to believe that there
is any flaw in
Lecture 9:
Introduction to QM:
Review and Examples
S1
S2
Lecture 9, p 1
1
2
4
0
e
V
n
m
2
E
photnK
.E
1
5
0
e
V
n
m
2
Summary: Photon & Matter
Waves
Everything
E = hf
p = h/
Light (v = c)
E = pc, so
E
Lecture 12:
Particle in 1D boxes
U(x)
(x)
U
n=2
n=0
U
n=1 n=3
x
Lecture 12, p 1
This week and last week are critical for the course:
Week 3, Lectures 7-9:
Light as Particles
Particles as waves
Probabi