UNM Physics 262: General Physics III
Optics, Relativity, and Quantum Mechanics

Announcements and updates

M Dec 18 Here is the summary gradesheet for the class, posted anonymously by CPS number. On the whole, they aren't too dissimilar from the earlier projections. The final exams have been graded and may be picked up in my office (Room 26, P&A building). I'll be in today until at least 4 p.m. I expect to be in most other days this week as well on a catch-as-catch-can basis. The extra credit portion of everyone's grade has increased because on the earlier gradesheet I erroneously counted only 0/1 for CPS incorrect/correct responses instead of 0/1/2 for CPS no/incorrect/correct responses.
I know each and every one of you put a lot of effort into this course, and I'm proud of you for that. The subjects we covered are very difficult and sometimes counterintuitive. For those of you continuing your physics studies, this is just the tip of the iceberg of a fascinating journey. For those of you for whom this is a terminal physics course, I hope you have learned that even the most bizarre phenemona can be tackled with a rational problem-solving approach. Best wishes to you all and have a happy holiday season.
M Dec 11 I've had some e-mails asking me, "What resource materials are allowed for the final exam?" To remind everyone what I said in class, I'm writing it down here. You can bring a SINGLE 8.5" x 11" piece of paper, with writing on both sides if you so desire, to the exam. You may also bring a ruler, but rulers will be provided if you don't have one. The same goes for pens/pencils---extras will be available at the exam if yours breaks for some reason. What you cannot use during the exam is either a calculator or a cell phone. If you use either one of these on the final, you will get a zero for the exam. The exam consists of eight questions surveying the entire course, one of which I announced on the last day of class. My best recommendation for studying is to do practice problems, especially in the areas you had a hard time with during the midterm exams.
F Dec 8 Here is an outline review of the main topics we discussed in the course. We will go over it in class today.
Th Dec 7 The solutions to exam 3 are now available on the course website. Please take the time to review the solutions to all actual and sample exams as well as all the problem sets as you prepare for the final exam. I reposted a few of them recently to correct some type-os here and there so you may want to download the most recent versions.
Th Dec 7 Here is a summary gradesheet, histograms, and detailed problem set gradesheet for the course, posted by CPS number. Please verify that all the individual information is complete and correct. To arrive at a total current grade, I assumed a grade on the final exam equal to the average of the first three midterms. Exams will be returned in class tomorrow.
Th Dec 7 Graded problem set 12 has been returned to your mailbox outside the lecture hall and exam 3 has been graded. I will post an anonymous complete list of grades for the entire course so far soon with an estimate of final grades, assuming that final exam performance is equal to the average performance of the three midterm exams. Solutions to exam 3 will be posted soon as well.
W Dec 6 Here are some links to quantum well and tunneling demos. STM images from nobel.org, a Java Applet from France and a Java Applet from Colorado.
M Dec 4 During final exam week, I will be holding extended office hours. They will be in my P&A office, room 26 at the following times: Monday 12-2 p.m., Wednesday 12-1 p.m., Thursday 2-4 p.m. If you have any questions, please take the opportunity to stop by.
Th Nov 30 Solution Set 12 and a repost of Solution Set 11 (with corrections) are now on the course website to assist you in studying for the midterm exam. Please take the time to read through them, and more importantly to do the sample exam.
T Nov 28 I reposted the sample midterm exam 3 and the corresponding solutions because they contained some mistakes that I corrected real-time during the review session. I guess that's what happens when I rush a write-up over a couple of slices of pizza at Saggio's. Everything should be correct now.
Su Nov 26 Here is a listing of the grades for exams 1 & 2 and problem sets 1-9, posted anonymously by CPS number. Please check your records and let me know if there are any incorrect entries.
Su Nov 12 Problem set 10 clarification: Because the normal to the Earth's surface is taken to be radially outwards in problem 10.3 a, the flux of the Sun's radiant power striking the Earth is negative. The minus sign should be associated with the power itself, not the area you are asked to calculate in this problem. So please report a positive area for this question. I reworded the problem so that the minus sign was pulled out of the integral to make this point clearer.
Th Nov 9 In my haste to cut and paste data from the two columns of my spreadsheet containing the exam 2 grades in four side-by-side columns so that it would conveniently be all on one page, I accidentally shifted the grades relative to the CPS numbers by two after CPS number 31. I have reposted the grade table in a long two page document without making any attempts to make it look nice. Just be sure to read on to page two if you don't see your CPS number on the first page.
Th Nov 9 Here is a histogram of the (scaled) scores on the relativity midterm exam. Here is a more detailed grade listing, posted anonymously by CPS number. Midterm exams will be returned in class on Friday. Also, remember that there is a problem set assigned this week, Problem Set 10.
M Nov 6 Here is a selected history of the photoelectric effect. Much is left out, but some highlights are there.
M Oct 23 I added the diagram to problem 8.2 and fixed a minus sign error in problem 8.1b this weekend, along with a couple of spelling errors. Everything else with Problem Set 8 is fine.
M Oct 16 Two minor type-o corrections for Problem Set 7: In problem 7.1 a, it now correctly says that 8c is equal to the distance traveled by the Enterprise in the original IRF divided by the proper time passed on the Enterprise, rather than the proper time passed on the Enterprise divided by the distance it travels as measured in the original IRF. Sorry for the confusion! Also, in problem 7.3 b, event 5 should be "Light from event 4 reaches Arthur," not "Light from event 3 reaches Arthur." Event 3 is itself light reaching Arthur, so clearly there was a type-o here.
Th Oct 12 I updated Problem Set 7 with a few corrections: Now the problem numbers are correct, a type-o in a number in the first table of problem 7.4 has been corrected, and the hyperbola diagram for you to trace over for problem 7.4 has been added.
W Sep 27 Here is a link to Einstein's famous E = mc^2 paper from 1905. Here it is in English. The title of the paper is "Does the inertia of a body depend on its energy content?" and was published exactly 101 years ago today.
Su Sep 24 Some students have asked me how their problem set scores stand in relation to the overall class performance. Here is a PDF of a histogram of problem set grades for the course so far, based on the first three problem sets. With the lowest grade dropped (as will be the course-end policy, stated below), the median is 60% whereas without the lowest grade dropped, the median is 49%. The corresponding means are 54% and 46%. From the overall look of the histogram, I'd say that if you are doing 45% or better on your best two problem sets, you are keeping pace. In any event, homework is only a small portion of your overall grade so don't fret too much about this. Some of you have extra credit of up to 5% to add to your overall grade as well.
F Sep 22 Here is an egregious link to some freaky optical illusions generated using spatial frequency filters, the kind you get using the diffraction ideas we talked about in class. Watch out for freaky cat-lady!
Th Sep 21 The practice optics midterm solutions are now posted. To get the most value out of this resource, spend the time going through the sample midterm yourself before looking at the solutions; don't just check after you work each problem.
Th Sep 21 I've posted a sample exam for you use to help you prepare for the optics midterm. I'll post solutions before the weekend. For those attending the review on Sunday, please work through these so we can talk about them.
W Sep 20 I've posted notes on reflection and transmission and coherence that are not in the textbook but were covered in lecture. I've also posted the first page of the first midterm exam (on optics) which contains the instructions for the exam. If you read them ahead of time, you'll save yourself some time on exam day!
M Sep 18 I've posted the next (short) Problem Set 5 early in case you'd like extra time to work on it. It is only two problems and is due on W Sep 27, after the exam.
T Sep 14 Here's a link to a Wave Applet to help you visualize some of the concepts we will be talking about.
W Sep 13 Homework Extension: Problem set 3 is now due on F Sep 15. Problem set 4 assigned today is still due on W Sep 20.
Th Sep 7 Part (e) of question 3.6 in Problem set 3 has been simplified.
M Sep 4 As mentioned in class, I will be holding special office hours this week because of the holiday. My office hours will be in Regener Hall 114 on Tuesday, Sep 5, from 9:30 a.m. - 10:30 a.m.
T Aug 29 Notes from Lecture 4, covering the proof that EM waves are transverse and have orthogonal E and B fields posted. (See below.)
M Aug 28 Summary of all of physics circa 1905 posted. (See below.)
T Aug 22 TA office hours and SI session moved to RH 111. Ph 262L dates corrected to W/Th. Explicit extra credit formula added. Problem set 1 has been posted to this website (see below).

Course description

This course covers three major areas of physics: electromagnetic waves and optics, special relativity, and quantum mechanics. These are some of the more exciting areas of physics with many nonintuitive results. Emphasis will be on developing intuition through examples and problem solving.

General course information


Dr. Andrew Landahl (alandahl@unm.edu)
Room 26, Physics and Astronomy
(505) 277-1287

Teaching Assistant

Alexandre Tacla (tacla@unm.edu)
Room 111, Regener Hall
Office for Tue. 1:30-2:30 p.m. only

Class schedule

Time Mon Tue Wed Thu Fri
12-12:50 Physics 262
(RH 103)
Physics 262
(RH 103)
Physics 262
(RH 103)
1-1:50 Office Hours
(RH 111)

TA Off. Hrs.
(RH 111)
2-2:50 Physics 267
(RH 114)
Physics 262L
(RH 119)
Physics 262L
(RH 119)
SI Session
(RH 111)


Physics 262: MWF 12-12:50, RH 103
Physics 267: M 1-1:50, RH 114
SI session: T 2:30-3:20, RH 111

Physics 262L: W/Th 2-4:50, RH 119
Office Hrs.: M 1:00-1:50, RH 111
TA Off. Hrs.: T 1:30-2:30, RH 111

Required Items

University Physics, 11th Ed., Young & Freedman Special Relativity, Ohanian eInstruction CPS clicker

Optional Items

Spacetime Physics, 2nd Ed., Taylor & Wheeler The Feynman Lectures on Physics, Feynman, Leighton, and Sands

Prerequisites and corequisites

Prerequisite: Physics 161. Pre- or co-requisite: Math 264.


Problem sets (25%), best 2 midterms (50%; 25% ea.), final exam (25%).
Extra credit: 5% max total from problem sets, CPS quizzes, weekly problem session attendance.
Extra credit formula: EC/5% = min(1, (EC PS)/(EC PS total) + CPS/(CPS total) + (267/SI weeks attended)/(267/SI total weeks)).

Problem sets

Handed out Wednesdays, due the following Wednesday by 5 p.m. Hand-in cart provided in classroom. Otherwise box in Physics and Astronomy main office must be used. Lowest problem set grade dropped; late problem sets not accepted. Solutions posted to website and glass cases outside Regener 114. Homework returned in boxes outside Regener 103 by CPS number. Your box is your CPS number plus 952. Keep your CPS number private! Homework can be signed by CPS number if desired.

Exam schedule

Midterms during class on Sep. 25, Oct. 30, and Dec. 1. Final in classroom on Dec. 15 from 10 a.m. - 12 p.m. Lowest midterm dropped; no midterm make-ups. I will hand out final exams 1 hour early at 9 a.m. for those who would like more time. Graded final exams available Dec. 18 from 9 a.m. - 2 p.m. in my Physics and Astronomy office, room 26. Students with special exam needs should coordinate through Accessibility Services in Mesa Vista Hall (277-3506).

CPS quizzes

CPS class key: F20740H691. Responses credited 0/1/2 points for no/incorrect/correct answer. CPS clickers must be registered before class on Monday, Aug. 28; points credited from then forward. CPS technical assistance available from Cathy Webster (webster@unm.edu). The first four weeks of the term, she will hold office hours in Regener 111 on MF 9:30-12:30, T/Th 10:00-1:00, and W 11:30-2:30. For an online FAQ of the CPS system for UNM students, see http://www4.unm.edu/physics/help/students.


Electromagnetic waves

Faraday's law, displacement current, Maxwell's equations (YF 29.1-7)
EM wave equation, Poynting vector (YF 32.1-7)
Reflection, refraction, dispersion, polarization (YF 33.1-7)

Geometric and Physical Optics

Mirrors, images, reflecting surfaces, thin lenses, optical instruments (YF 34.1-8)
Interference, diffraction, holography (YF 35.1-5, 36.1-8)

Special relativity

Reference frames, Galilean relativity, experimental contradictions (OH 1.1-7)
Einstein's postulates, synchronization, spacetime diagrams (OH 2.1-3)
Spacetime interval, Lorentz transformation, kinematics (OH 2.3-6)
Time dilation, relativistic Doppler shift, length contraction (OH 3.1-4)
Twin paradox, pole-in-barn paradox, other paradoxes (OH 3.5-6; other material)
Relativistic mechanics: momentum, force, energy, four-vectors (OH 4.1-5)
Electromagnetism in relativity (OH 6.1-4)

Quantum mechanics

Line spectra, blackbody radiation, photoelectric effect, Compton scattering (YF 38.1,3,8,2,7)
de Broglie wavelength, electron diffraction, Rutherford atom, double-slit experiment, Bell inequalities and entanglement (YF 39.1,2,38.4,9,39.3, other references)
The Schroedinger equation, wells, barriers, oscillators (YF 39.5,40.1-4)
H atom, angular momentum, Zeeman effect, spin, (YF 41.1-3)
Identical particles, exclusion principle, periodic table (Other references)

Lectures and Problem sets

M Aug 21 Course overview, electrostatics and magnetostatics review (YF 21-28)
W Aug 23 Faraday's Law, Lenz's Law (YF 29.1-5)
Problem Set 1
Solution Set 1
F Aug 25 Faraday's Law applications, magnetic energy (YF 29.6, 30.2-3, 31.6)
M Aug 28 Displacement currents, Maxwell's equations, EM plane waves (YF 29.7, 32.1-2; Notes on EM waves)
1905 Physics summary
W Aug 30 EM plane waves, EM wave energy and intensity (YF 32.2-6)
Problem Set 2
Solution Set 2
F Sep 1 EM wave intensity and momentum, radiation pressure, polarization (YF 32.4)
M Sep 4 Holiday - Labor day  
W Sep 6 Malus' Law, Snell's Law, total internal reflection (YF 33.1-5)
Problem Set 3
Solution Set 3
F Sep 8 Chromatic dispersion, Brewster's Law, point images (YF 33.1-5, 34.1-3)
M Sep 11 Imaging equations, lateral magnification, thin lenses (YF 34.1-4)
W Sep 13 Seeing images, reflection & transmission, interference. (YF 34.6, 35.1, Notes on r & t not in book)
Problem Set 4
Solution Set 4
F Sep 15 Optical path difference, phasors (YF 35.1,3-5)
M Sep 18 Phasors, thin films, coherence (YF 35.2-3)
Problem Set 5
(posted early)
Solution Set 5
W Sep 20 Spatial & temporal coherence (YF 36.7, Notes on some material not in book)
F Sep 22 Diffraction through a thick slit (YF 36.2-3)
Sun Sep 24 Midterm review session at 2 p.m. in 103 RH.  
First page of exam (instruction sheet)
SAMPLE practice exam
SAMPLE practice exam solutions
Midterm exam solutions
(YF 29,32-36)
W Sep 27 Relativistic mass, principle of relativity, reference frames (OH 1.1, 4.2 (results only))
F Sep 29 IRFs in NIRFs, Galilean transformation, addition of velocities (OH 1.2-4; IRFs in NIRFs not in OH)
M Oct 2 Principle of relativity violations, Lorentz transformation (OH 1.2-4; OH 2.4-6)
W Oct 4 Special Lecture: COBE and the 2006 Nobel Prize in Physics Problem Set 6
Solution Set 6
F Oct 6 Einstein's postulates, relativity of simultaneity, relativity of length (OH 1.2-3; OH 2.1-4)
M Oct 9 Invariance of transverse length, invariance of interval, time dilation, length contraction (OH 2.3, 2.4, 3.1, 3.4)
W Oct 11 Spacetime diagrams (OH 1.2, 1.3, 2.2, 2.3, 2.4)
Problem Set 7
Solution Set 7
F Oct 13 Holiday - UNM Fall Break  
M Oct 16 Spacetime diagrams, light cones & causality, Lorentz transformation (OH 2.2-4)
W Oct 18 Kinematics in special relativity (OH 2.5,2.6) Problem Set 8
Solution Set 8
F Oct 20 Twin Paradox (OH 3.2,3.5,3.6)
M Oct 23 Doppler shift (OH 3.2,3.3)
W Oct 25 Relativistic dynamics: momentum and energy (OH 4.1-4)
Problem Set 9
Solution Set 9
F Oct 27 Energy-mass-momentum relation, 4-momentum Lorentz transformation (OH 4.5-6)
Sun Oct 29 Midterm review session in 103 RH, 2:00 p.m.  
SAMPLE practice exam
SAMPLE practice exam solutions
Midterm exam solutions
(OH 1-4)
W Nov 1 Overview of quantum mechanics (YF 38)
F Nov 3 Blackbody radiation (YF 38.8)
M Nov 6 Blackbody radiation, Photoelectric effect (YF 38.8, 38.2)
W Nov 8 Thermionic emission, Bremsstrahlung, Compton effect (YF 38.7,38.3)
Problem Set 10
Solution Set 10
F Nov 10 Compton effect, line spectra (YF 38.3-5)
M Nov 13 Line spectra, nuclear atom, Bohr quantization (YF 38.3-5)
W Nov 15 Bohr quantization generalizations (YF 38.3-5)
Problem Set 11
Solution Set 11
F Nov 17 de Broglie wavelength, electron diffraction (YF 39.1-3)
M Nov 20 Heisenberg uncertainty, EPR paradox (YF 39.3-4)
W Nov 22 Complex arithmetic review, Schroedinger equation (YF 39.5,40.1-2)
Problem Set 12
Solution Set 12
F Nov 24 UNM Holiday - Thanksgiving  
M Nov 27 Solutions to the SE, particle-in-a-box (YF 40.1)
M Nov 27 Midterm review session at 7 p.m. in 103 RH.  
W Nov 29 Infinitely deep, finitely deep potential well problems (YF 40.1-2)
SAMPLE practice exam
SAMPLE practice exam solutions
Midterm exam solutions
(YF 38-40)
M Dec 4 3D potential wells, degeneracy, tunneling (YF 40.3,5)
W Dec 6 Tunneling, ICES course evaluation (YF 40.3)
F Dec 8 Review of topics in the course (YF 29-40;OH 1-4)
M Dec 11 No class - Final exam week (Office Hours)  
W Dec 13 No class - Final exam week (Office Hours)  
10 a.m - 12 p.m. (come early at 9 a.m. if desired)
(YF 29-40,OH 1-4)

Material on this site is subject to revision. Last updated: Dec. 7, 2006.