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, Cambridge University Press, 1984.


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 :








(Very) Preliminary course content and schedule (please check above for up-to-date weekly planning):



L1: Introduction. Review of classical physics

Chapter: 1-1



L2: Inertial observers / Galilean relativity




L3: Newton/Galileo/Maxwell




L4: Michelson-Morely




L5: Einstein’s Gedankenexperiments




L6: Relativistic kinematics




L7: Space-time diagrams


HW1 due


L8: Space-time diagrams




L9: Lorentz transformations




Problems class (HW1)


HW2 due


Problems class (HW2)




L10: Lorentz transformations




L11: Relativistic energy




L12: Relativistic dynamics


HW3 due


Problems class (HW3)




L13: Paradoxes




L14: Elementary particles

13-1, 13-2



L15: Accelerated reference frames


HW4 due


Problems class (HW4)




L16: Origins of quantum theory: quantization of charge




L17: Light – particles or waves? Photoelectric effect




L18: X-ray scattering / Compton effect


HW5 due


Problems class (HW5)




L19: Introduction to statistical physics / black body radiation




L20: Planck and the black body I

3-2 (not quite enough detail in the book)



L21: pre-exam review




Midterm I 




L22: Planck and the black body II




L23: Midterm I discussion




L24: The structure of the atom – Rutherford model


HW6 due


Problems class (HW6)

4-1, 4-3



L25: Electronic structure of atoms – Bohr model




L26: deBroglie matter waves – particle – wave duality




L27: Wave packets


HW7 due


Problems class (HW7)




L28: Heisenberg uncertainty principle




L29: Schrödinger’s postulates I




L30: Particle in a box / infinite potential well


HW8 due


Problems class (HW8)




L31: Transmission and reflection coefficients of waves I




L32: Transmission and reflection coefficients of waves II / Tunnel effect




L33: pre-exam review




Midterm II




L34: Finite square well potential (and applications)




L35: Discuss Midterm II




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


Problems class (HW9)




L37: Expectation values




L38: Harmonic potential well




Problems class (HW10)  (turnout is traditionally poor on this day…)


HW10 due


L39: 3D Schrödinger equation I




L40: 3D Schrödinger equation II




L41: Angular momentum and quantum mechanics




L42: Hydrogen atom




L43: Magnetic moments of atoms / spin


HW11 due – EXTRA TIME!!!


L44: Zeeman effect / Pauli exclusion principle




Problems class (HW11)




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.





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 Utah.


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

  • PHYS 2220 and MATH 2250

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

  • The problems classes, which are run by the TA, will usually take place on Fridays. Check the complete schedule above.

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.




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!




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

  • 2 midterms (15 % each), final (30 %), homeworks (35 %), quizzes (5 %)

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 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) ( 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.