Physics 3740 : Introduction
to special relativity and quantum mechanics
Schedule: Location:
Instructor: John Lupton, JFB 307 (Phone: 581-6408)
Teaching Assistant:
UPDATED Tuesday,
January 05, 2010.
-----------PLEASE BE SURE TO PRESS RELOAD! -------------
Note: There’s a mistake in the text! Relativistic
velocity transformations on p. 22, equ. 1-22:
the uz´ should read ux
rather than uz in the denominator. The
equation is correct in the 4th edition of the book. Thanks for
pointing this out.
Course outline
The goal of the course is to provide you with an introduction to the revolution of physics which occurred at the onset of the 19th century. Much of classical physics is based on logical deduction and common sense. As we will see, logical deduction can take us beyond “common” sense, testing our own understanding of our very own intuition - why can nothing move faster than the speed of light? How can time be relative? Why are energy and mass equivalent? How can a particle be a wave … be a particle? How can we be uncertain about seemingly certain things? Why is our seemingly continuous nature discrete?
Modern Physics is about challenging your own intuition. It is all about invoking the powers of logical, conclusive deduction. It is about challenging what you are told to be absolute truths by carefully conceiving counter examples. It is about applying the foundations of scientific methodology, making observations, formulating hypotheses, and testing these with further observations. It is about the power of experimentation, the trust we place in observation. It is not (primarily) about learning lots of equations off by heart. I hope you will be able to share some of the enthusiasm which keeps on driving us professionals over one hundred years later.
General remarks
At the last count, we had 17 physicists, 3 chemical/mechanical/electrical engineers, 3 mathematicians, 1 chemist, 1 computer scientist, and several undeclared majors registered for the course, ranging from freshman to senior. As you will appreciate, it is not trivial to pitch the course to meet all desires. Fortunately, it’s a reasonably small class, so we may be able to make some adjustments in pace and scope. If you find you’re getting behind, don’t just “bottle it up”, come and speak to me or the TA.
It is your responsibility to ask questions!
This is a reasonably demanding class, mostly because we’ll be covering so many different topics and you’ll have to do quite a bit of reading on your own. I expect you will take roughly 10 hours/week for this class (there are 4 hours of instruction, 4-5 hours for the homeworks, and 1-2 hours to go through your notes and do some reading).
I strongly urge you to avoid missing (too many) classes. Also, try to stay on top of the homeworks. The exam questions will be easier than the homework questions, but you’ll get a lot of credit for the homework.
Recommended text
Modern Physics, by P. A. Tippler and R. A. Llewellyn (please take note that there have been some concerns raised by former students with regard to this book. I think it’s OK, but you may want to check out the others.) The 5th edition has only just come out. You may be able to get hold of the 4th edition instead – I don’t think it is going to make much difference to you (the 5th edition seems to have a better binding).
Further reading
Modern Physics, J. Bernstein, Prentice Hall, 2000
Introduction to Quantum Mechanics, B. H. Bransden and C. J. Joachain, Longman Scientific / Wiley, 1989
Molecular Quantum Mechanics, P. W. Atkins, Third edition, Oxford University Press 1998.
Modern Physics, K. Krane, Second edition, Wiley 1996
Concepts of Modern Physics, A. Beiser, Sixth edition, McGraw-Hill, 2003
Modern Physics for Scientits and Engineers, J. R. Taylor, Second edition, Prentice Hall 2004.
An Introduction to Quantum Physics, A. P.
French,
Current reading:
Weekly schedule (this is to give you a rough idea of what’s coming):
Problem sheets and handouts
General remarks: The problems are designed to get you thinking about the material you heard about in the lectures (and should encourage you to read along/ahead a little, too!). I expect attempting all 4 will take 4-6 hours. Some of the problems may be a little more tricky, so don’t panic, just take this as a challenge and a possibility to dive further into the material. Don’t forget, you can still get full marks even if you don’t attempt all of the problems (see below!). There will not always be perfect agreement between what we cover in the lecture and the problem sheets. This is an advanced course and you are strongly encouraged to read along in the text and now and again even run ahead a little.
Problems will generally be posted on Wednesdays, solutions on Fridays after the problems class.
Quizzes :
Exams:
(Very) Preliminary course content and schedule (please
check above for up-to-date weekly planning):
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L1: Introduction. Review of classical physics |
Chapter: 1-1 |
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L2: Inertial observers / Galilean relativity |
1-1 |
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L3: Newton/Galileo/Maxwell |
1-1 |
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L4: Michelson-Morely |
1-1 |
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L5: Einstein’s Gedankenexperiments |
1-2 |
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L6: Relativistic kinematics |
1-3 |
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L7: Space-time diagrams |
1-4 |
HW1 due |
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L8: Space-time diagrams |
1-4 |
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L9: Lorentz transformations |
1-3 |
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Problems class (HW1) |
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HW2 due |
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Problems class (HW2) |
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L10: Lorentz transformations |
2-2 |
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L11: Relativistic energy |
2-1 |
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L12: Relativistic dynamics |
1-6 |
HW3 due |
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Problems class (HW3) |
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L13: Paradoxes |
1-6 |
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L14: Elementary particles |
13-1, 13-2 |
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L15: Accelerated reference frames |
2-5 |
HW4 due |
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Problems class (HW4) |
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L16: Origins of quantum theory: quantization of charge |
3-1 |
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L17: Light – particles or waves? Photoelectric effect |
3-3 |
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L18: X-ray scattering / |
3-4 |
HW5 due |
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Problems class (HW5) |
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L19: Introduction to statistical physics / black body radiation |
8-1 |
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L20: Planck and the black body I |
3-2 (not quite enough detail in the book) |
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L21: pre-exam review |
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Midterm I |
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L22: Planck and the black body II |
3-2 |
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L23: Midterm I discussion |
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L24: The structure of the atom – |
4-2 |
HW6 due |
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Problems class (HW6) |
4-1, 4-3 |
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L25: Electronic structure of atoms – Bohr model |
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L26: deBroglie matter waves – particle – wave duality |
5-1 |
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L27: Wave packets |
5-3 |
HW7 due |
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Problems class (HW7) |
5-5 |
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L28: Heisenberg uncertainty principle |
6-1 |
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L29: Schrödinger’s postulates I |
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L30: Particle in a box / infinite potential well |
6-2 |
HW8 due |
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Problems class (HW8) |
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L31: Transmission and reflection coefficients of waves I |
6-6 |
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L32: Transmission and reflection coefficients of waves II / Tunnel effect |
6-6 |
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L33: pre-exam review |
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Midterm II |
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L34: Finite square well potential (and applications) |
6-3 |
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L35: Discuss Midterm II |
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L36: Double potential well |
6-3 / 6-6 (this combines both chapters. The book does not go into as much detail in coupled wells – this is just the finite well + tunneling) / 9-2 |
HW9 due |
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Problems class (HW9) |
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L37: Expectation values |
6-4 |
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L38: Harmonic potential well |
6-5 |
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Problems class (HW10) (turnout is traditionally poor on this day…) |
7-1 |
HW10 due |
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L39: 3D Schrödinger equation I |
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L40: 3D Schrödinger equation II |
7-1 |
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L41: Angular momentum and quantum mechanics |
7-2 |
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L42: Hydrogen atom |
7-3 |
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L43: Magnetic moments of atoms / spin |
7-4 |
HW11 due – EXTRA TIME!!! |
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L44: Zeeman effect / Pauli exclusion principle |
7-8 |
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Problems class (HW11) |
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L45: Revision Also note: I intend to offer a lab tour at the end of class. I will ask in the course of the week to see if anybody is interested. |
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Important dates
Some (helpful?) links
Einstein’s FBI file
David Morin’s lecture notes on mechanics and relativity at Harvard.
Most of the images I show in the lecture are either from the book or from Wikipedia.
Regarding Boltzmann statistics and temperature, you may want to check out our recent patent.
Jim Carrey on Quantum Mechanics.
Hands-on quantum mechanics in
You may like to try this Hyperphysics website: Quantum Mechanics and Relativity are the most relevant items.
And finally, if you need some motivation as to why you are studying, check out this Op-Ed from Friedman in the New York Times.
Recommended Prerequisites
You’ll probably be OK with the
relativity part with high school maths, but we really
won’t get round using some more complex formalisms
later on. You shouldn’t be scared by partial differentials, chain rule, basic
differential equations, complex numbers, etc.
Problems class
You are strongly
encouraged to participate actively in the problems class and present
your solution to the problem on the board. Besides allowing you to develop your
presentation skills we will also raise your score for this particular
problem by up to a factor of 2 for a correctly solved problem
on the board (you can do this up to 4 times in the semester). This means less
pressure for you in the exams!
Office
hours
TA: .
These
office hours are only suggestions! Let us know if there are any
scheduling conflicts.
Homework
There
will be 11 sets of homework, typically consisting of 3 problems. Don’t panic if
a problem appears too difficult or if you really get stuck – the sheet is
designed to offer something for everyone! An additional problem labeled by a
(*) allows you to go into more depth and accumulate extra points (an extra 20
or 30 %, depending on difficulty). I will hand out the new problems sheets on
Fridays. Homeworks are to be handed in at the lecture
on the following Friday.
The
marked homeworks will be returned in the problems
class on the following Monday and discussed.
While
you are strongly encouraged to interact and discuss problems with fellow
students, the homeworks count towards your final
grade and must be prepared individually. It is remarkably easy to
spot all too intensive collaboration on homeworks!
Exams
There
will be two midterm exams and one final exam. You will be allowed to take one
sheet of paper with you to the exams.
There
will be no re-sit exams – please make sure you make it to the exams. Let me
know of any scheduling conflicts immediately!
I also
intend to do four 10 minute quizzes throughout the semester. These quizzes will
be announced in the lecture before and on the web page.
Grading
Scheme
To a certain extent, grading will be comparative, i.e. your grade will depend on the performance of your peers. If the total points scatter by a factor of 4 (as has previously been the case), it is unlikely everyone will be able to get a B… Grading is a classical example of the “prisoner’s dilemma”, to which quantum mechanics actually provides an innovative solution…
Academic
Integrity
The
policy on academic integrity (Student Behavior Code) can be found on the
University web site at http://www.admin.utah.edu/ppmanual/8/8-1.html.
The student is responsible for reading and understanding this policy. The
Student Behavior Code will be strictly followed in this class.
Students
with Disabilities
The
University of Utah Department of Physics seeks to
provide equal access to its programs, services and activities for people with
disabilities. If you will need accommodations in this course, reasonable prior
notice must be given to the instructor and to the Center for Disability
Services, 162 Olpin Union Bldg, 581-5020 (V/TDD) (http://disability.utah.edu/) to make
arrangements for accommodations. You are strongly encouraged to come and talk
to the instructor about your disability and necessary accommodations within the
first two weeks of the semester.
If you have any concerns or impediments whatsoever DO NOT wait until AFTER the exam to inform us.