Homework: I'll assign weekly problem sets, due Thursday @ 11:59 pm. You may leave your homework in my mailbox near the physics department office, or of course you may give it to me personally (please do NOT leave it in the box beside my office or stick it under my door). Homework submitted late without prior arrangement will receive a 50% penalty if submitted within three days of the due date (i.e. by Sunday @ 11:59 pm), and will not be accepted after that.
Why do the homework?
I can't emphasize enough the importance of working the problems.
In some of your
classes homework is primarily evaluative; the point is for you to
demonstrate what you've learned from the readings and lectures. In physics
the homeworks are primarily instructional;
you learn physics primarily by doing working problems.
You must work the
problems, think about the results, and understand any mistakes you've
made if you wish to attain the type of understanding of the subject
required of a working physicist. In at nutshell:
If you can't work problems you don't know physics.
I (or a grader) will grade the problems,
and I'll hand out solutions. I encourage
you to read the solutions and understand any mistakes immediately.
If it doesn't
make sense, ask me about it right away---don't wait
until right before an exam.
Extensions
If you've got a compelling reason why you need an extension,
come talk to me in advance.
I will not grant a homework extension without penalty if you ask for
it on the day the homework is due, so don't ask for one.
[If you need such a last-minute or post-facto extension due
to extenuating circumstances (e.g. death in the family, sudden
illness, travel problem), you'll need to have the Dean of Students
or your Class Dean formally make such a request to me and suggest
a rescheduled due date. You should also take this route if you
need an extension but you don't want to tell me why (say, it's for
personal or legal reasons). If you explain your reason to a Dean
and the Dean tells me it's OK, that's good enough for me.]
In general, though,
life will be easier for you and for me if you get into the habit
of doing your best to finish the problem set on time and handing
in as much as you've been able to complete by the deadline.
The College requires that all written work for a course except for a final be submitted by 5 pm on the last day of classes. The physics department takes this deadline seriously. After that day/time, no homework or lab reports will be accepted, nor will I conduct exit interviews for labs.
The roles of lectures and textbooks
Lecture will not be a regurgitation of the text, a summary of all
you need to know for the course, or a how-to guide for the homework.
Rather, I'll try go deeper into selected points.
In lecture I'll cover material and do demonstrations
related to the readings, but I won't feel obliged to
be comprehensive in those places where I feel the text is adequate
and I may focus only on a few points that I feel are particularly
interesting or subtle. You shouldn't expect to understand what's
going on without close study of the readings, and you
should come to class with questions you have
on the readings. Further, after we settle into the semester
a bit, I expect the classes will become less lecture-oriented
and more participatory; it will be difficult to reap
the maximum benefit from that format if you're not
sufficiently prepared to fully participate.
For the problems you can't solve, talk to classmates, attend the problem sessions, or ask me. When you ask me, either try to give you just enough of a hint to get you through, or I'll guide you through the problem with a series of leading questions. I'll never just tell you how to do it. If you run out of time and don't finish the set, start earlier next week. When the solutions come out, look over them right away, before you've forgotten all of the points you were confused about. You think you'll just get clear on it before the next exam, but there's never as much time as you think.
On the other hand, if you find the class too slow for your liking, if you have questions that you aren't getting answers to, if you'd like more detail, if you are frustrated that we aren't digging deeply enough, if you crave more applications, come talk to me. I'm very happy to provide you with additional materials or explanations that will will stimulate you and challenge you at whatever level you can handle.
One word of warning: Amherst College students tend to have lots of extracurriculars of all types. I support this (enthusiastically), and I am occasionally willing to be flexible to facilitate your participation in range of activities, but don't let your extracurriculars overshadow your academics. If you become concerned that your courses are getting in the way of your extracurriculars, you definitely have the wrong mindset. Remember why you're here.
If circumstances in your life beyond the class are the problem, you can come talk to me, but also talk to your class Dean.
Key derivations / chains of logic / results to commit to memory
Mathematica Tutorials
We will use Mathematica 5.2 at least occasionally in the homework,
to obtain numerical solutions to problems that are not
analytically solvable and to simplify plotting of results.
If you've never used Mathematica before, or haven't used it much,
the tutorials will help you get started.
They were written by Professor Hilborn and revised by
Rebecca Erwin '02. If you download the file and save it to the
desktop with a .nb suffix in the name, your computer will recognize it
as a Mathematica notebook and will start up Mathematica automatically
when you double-click on the icon,
provided you have Mathematica installed. Mathematica is installed on
lots of the college's public machines, including
on the computers in the Physics
Department computer lab. Alternately, you can pay the $140 or so
to buy the student version.
| Week | Notes | Hmwk | |
| 1. September 5 | Cutting deals... Sept 7: Introduction to the course General course information. Coulomb's law. Gauss's law. |
Read: Review Griffiths E&M Problems: Griffiths E&M: 1.60, 1.61, 1.62, 2.47, 2.49, 3.14 (just a few review problems from Griffith to warm you up) [Due Sept. 15] |
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| 2. September 12 | E&M Redux: Electrostatics and Magnetostatics Sept 12: Electrostatics Differential form of Gauss's law. Electrostatic potential. Poisson's equation. Electrostatic field energy. Magnetostatics: Charge conservation. Lorentz force law. Biot-Savart law. Magnetic Gauss's law. Sept. 14: Magnetostatics Ampere's law (for magnetostatics) from Biot-Savart law. Analogs between electrostatics and magnetostatics. Vector potentials: Ampere's law in terms of vector potentials. Gauge transformations. Analog of Poisson's equation for magnetostatics. Electrodynamics: Local conservation of charge. Lenz's law and Faraday's law. Sept. 14 (3:30-4:30): Talks Sarang Gopalakrishnan: Michael Foss-Feig: A guide to Local Swimming Areas, and also a short bit of physics on Molecular Magnets |
Read: Review Griffiths E&M Problems: Griffiths: 5.38, 5.43, 5.51, 7.50, 7.59, 7.60, 8.12, 9.33 [Due Sept. 22] |
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| 3. September 19 | E&M Redux II: Electrodynamics / Special Relativity Sept 19: Electrodynamics Differential form of Faraday's law. Magnetic field energy. Maxwell-Ampere law. Full set of Maxwell's equations. Electromagnetic plane waves: form of the solution, dispersion relation, phase velocity. Maxwell's equations in terms of vector potentials: Redefine scalar potential for electrodynamics. Express E and B in terms of scalar and vector potential using magnetic gauss and faraday. Electric gauss and Maxwell-Ampere in terms of potentials (looks ugly). Sept. 21: Gauge invariance / Conservation Laws / Special Relativity Gauge invariance of maxwell eqns. (expressed in terms of potential). Coulomb gauge, Lorentz gauge, and their virtues. Conservation laws: Poynting's theorem and the conservation of energy. Momentum conservation and the maxwell stress tensor. Special relativity: the fundamental postulates. Sept. 21 (3:30-4:30): Talks Speaker: Jason Merrill The maser as a reversible heat engine American Journal of Physics, Vol. 73, No. 1, pp. 63-68, January 2005 Jason's slides can be found at: Jason's slides Slide system S5 is at: S5 Provocateur: Mike Borkowski Speaker: David Stein The charge distribution on a conductor for non-Coulombic potentials American Journal of Physics, Vol. 69, No. 4, pp. 435-440, April 2001 Provocateur: Michael Foss-Feig |
Primary reading: Landau, Chap. 1, and start Chap. 2. Some suggested supplementary readings: Griffiths, Chap. 12, Jackson, Chap. 11. [The supplementary reading aren't necessary, but they may provide a different perspective on the material than Landau's or my own.] Problems: By popular demand, I have taken these from Jackson (3rd ed.). Work problems 11.4, 11.5, 11.6, 11.11. (I'll LaTeX these up if I can. For now, help yourself to photocopies of the problems from Jackson, Chap. 11 which are are available in the blue box outside my office. Also, the book is on reserve at the science library.) [Due Oct. 6] |
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| 4. September 26 | Special Relativity Sept. 26: Invariant Intervals Two postulates of special relativity. Consequence: loss of simultaneity. Define the interval in Minkowski spacetime as that which is null when events are connected by light rays. Show that this interval is invariant under LT. Example: examine case in which two events happening at the same place in some frame (timelike separation). Sept. 28: Lorentz transformations Spacelike interval implies there's a frame in which events are simultaneous, and vice versa. Light cone divides Mink. space into three regions: absolute past/future, elsewhere, a light cone itself. Proper time is time clock reads in its rest frame. Outline of twin paradox. Derive explicit form of most general linear transf. that leaves interval invariant (Lorentz transf.) in terms of rapidity. Observe: form is reminiscent of rotation. Obtain explicit form of LT in terms of v. Show primed axes on spacetime diagram. Sept. 28 (3:30-4:30): Talks Speaker: Mike Borkowski Feynman's scandalous proof of Maxwell's equations (based on AJP March 1990 Volume 58, Issue 3, pp. 209-211) Provocateur: Jason Merrill Speaker: Ben Heidenreich Symmetry and Magnetoelectric Effects (based on J. App. Physics Supplement to v. 33, no. 3 (March 1962) 1126-1133, "Magnetoelectric Effects in Antiferromagnets", G. Rado and V.J. Folen) Provocateur: Sarang Gopalakrishnan |
Read: Start Landau, Chap. 2 Problems: Jackson, Chap. 11: 4, 5, 6, 11 carried over from last week. [Due Oct. 6] |
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| 5. October 3 | 4-vectors and 4-tensors Oct. 3: Special relativity / 4-vectors and 4-tensors Inverse Lorentz transformation by switching sign of v. Galilean transformations commute, Lorentz transformations don't in general. Time dilation. Length contraction. Velocity addition. Example: radiation from relativistic particle into forward cone. Geometrical underpinnings of vectors and tensors. Physical laws expressed in 4-tensor form automatically satisfy first postulate of SR. Contravariant 4-vector, 4-tensor defined. Covariant 4-vector, 4-tensor defined. Express in index notation the fact that the product of LT and inverse LT is identity. [References: Arfken, Chap. 2 is an OK ref. for tensors from a non-geometrical perspective. However, he is concerned primarily with tensors in Euclidean 3-space, where the transformation of interest is rotation. It turns out that there's no need for him to maintain a distinction between covariant and contravariant indices in this case, and he doesn't. For a more geometrical approach, look at the first part of most books on general relativity.] Oct. 5: Tensor algebra and calculus Mixed tensors. Tensor algebraic operations: sum, outer product, contraction (esp. to form Lorentz scalars). Parity transformation. Physical laws expressed in tensor form are manifestly covariant (satisfy 1st postulate). Quotient rule. Levi-Civita tensor (actually a pseudotensor). Dual of a tensor. Metric tensor relates covariant and contravariant vectors. Define inverse metric with raised indices. Norm of 4-vector in terms of metric. Form of metric from metric equation. Metric form in invariant in all IRFs. Proper LT have det=1, improper LT have det=-1. Define covariant derivative as derivative wrt contravariant coordinates. Contravariant derivative is analogous. 4-vector divergence and D'Alembertian of scalar field are Lorentz scalars. Oct. 5 (3:30-4:30): Talks speaker: David Schaich provocateur: Ben Heidenreich speaker: Sarang Gopalakrishnan provocateur: David Stein |
Read: Landau, Chap. 1 and 2 Problems: Jackson Chap. 11: 10, 12, 13, 14, 15, 23 [Due Oct. 13] |
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| 6. October 12 | Covariant formulation of electromagnetism Oct. 10: Fall break Oct. 12: Maxwell equations in covariant form Volume in Minkowski space is Lorentz scalar. Covariant continuity equation. Four-current density of a point charge. Potential Maxwell equations in covariant form (in Lorentz gauge). Argue that E and B cannot transform as vectors, must be components of tensor. Oct. 12 (3:30-4:30): Talks speaker: Michael Foss-Feig speaker: Jason Merrill |
Read: Problems: |
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| 6. October 17 | Field transformations / Transformations as groups Oct. 17: Lorentz transformations of E and B fields Introduce field strength tensor F, express in terms of E and B. F is gauge invariant. F is a true tensor, second rank antisymmetric tensor. Introduce *F, the dual of F. *F is a pseudotensor. FF, and *F*F are Lorentz scalars, *FF is a pseudoscalar. Maxwell equations in terms of F and *F. Use F to show how E and B transform under LT. Oct. 19: Introduction to symmetry groups Abstract group defined (set with four properties: closure, identity, inverse, associativity). Example: rotations in plane. Representations of groups: realizations of group multiplication rule in terms of matrices (automatically satisfies associativity), i.e. homomorphism from group onto GL(n,R) or GL(n,C) (n is the dimension of rep). Faithful rep: homomorphism is an isomorphism. Equivalent reps: related by similarity transf. Unitary reps: all D(g) are unitary. Completely reducible, reducible, and irreducible reps defined. Permutation group (to be covered in detail by MB). Unitary group. Orthogonal group. Orthogonal group elements (in defining rep.) are matrices that rotate 3-vectors. Infinitesimal generators of rotations. Oct. 19 (3:30-4:30): Talks speaker: David Stein speaker: Mike Borkowski |
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| 7. October 24 | Continuous spacetime transformations Oct. 24: Rotations Exponentiating the inf. generator gives finite rotation (more generally, exp. the inf. generator gives the exponential parametrization of the group elements). Lie algebra defined. Closure of group under mult. means closure of vector space spanned by Lie algebra generators under commutation. SU(2) is 2-1 covering group of SO(3). Parametrize elements of SU(2). Explicitly map SU(2) into SO(3) (show for rotations about z-axis). Oct. 26: D-dimensional rotations and Lorentz transformations 2-1 relation between SU(2) and SO(3). Spinor reps of SU(2). Rotations in D-dim. Generators. Commutations relations. Oct. 26 (3:30-4:30): Talks speaker: Ben Heidenreich speaker: David Schaich |
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| 8. October 31 | Relativistic particle mechanics from action principles Oct. 31: Relativistic free particle: action Nov. 2: Relativistic free particle: motion, conservation laws Nov. 2 (3:30-4:30): Talks speaker: Sarang Gopalakrishnan speaker: Michael Foss-Feig |
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| 9. November 7 | Fields through action principles Nov. 7: Charged particles in external fields / a simple field theory Nov. 9 Nov. 9 (3:30-4:30): Talks speaker: Jason Merrill speaker: David Stein |
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| 10. November 14 | title Nov. 14: Nov. 16: Nov. 16 (3:30-4:30): Talks speaker: Mike Borkowski speaker: Ben Heidenreich |
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| 11. November 28 | title Nov. 28: Nov. 30: Nov. 30 (3:30-4:30): Talks speaker: David Schaich speaker: Sarang Gopalakrishnan |
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| 12. December 5 | title Dec. 5: Dec. 7: Dec. 7 (3:30-4:30): Talks speaker: Michael Foss-Feig speaker: Jason Merrill |
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| 13. December 12 | title Dec. 12: Dec. 14: Dec. 14 (3:30-4:30): Talks speaker: David Stein speaker: Mike Borkowski |
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| Finals week | Final exam: TBA |