Physics 125ab
Fall Quarter, 2007 and Winter Quarter, 2008
Course Homepage
Overview
The Ph125abc sequence covers quantum
mechanics
at a level of sophistication beyond the introductory Ph 2/12
sequence. You will see much material that is familiar to you from
these courses; but, in Ph125abc, you will truly learn to attack basic
quantum problems from scratch and arrive at
full solutions that can be tested by experiment. We will also
explore some of the interesting and unusual implications of quantum
mechanics.
It is impossible to emphasize how important the core physics courses Ph106 and Ph125 are: these teach you the basic frameworks and techniques that you must know to do any physics.
Ph125ab will cover the basic techniques and results of quantum mechanics along with a small selection of special topics.
Ph125c will cover additional applications and will be taught by Prof. Cross.
It is impossible to emphasize how important the core physics courses Ph106 and Ph125 are: these teach you the basic frameworks and techniques that you must know to do any physics.
Ph125ab will cover the basic techniques and results of quantum mechanics along with a small selection of special topics.
Ph125c will cover additional applications and will be taught by Prof. Cross.
Quick Links
- Announcements
- Vital Information
- Textbook(s)
- Lecture Strategy
- Problem Set Policies
- Grading
- Syllabus and Schedule, Lecture Note References, Problem Sets, and Solutions
- Exams
- Practice Problems
Announcements
- 2008/03/26
- Final exam scores available in anonymous grade sheet.
- Final exams available for pickup.
- PS14 available for pickup.
- 2008/03/24
- Final exam solutions posted.
- Final grades should be available on Wed Mar 26.
- 2008/03/13
- Final exam posted.
- PS14 solutions posted (updated
2008/03/14 -- typos in some spectroscopic terms in Problem 4).
- 2008/03/12
- Lecture 49 (Hartree-Fock, 3/12), updated lecture notes, and Review for Final posted.
- Also posted "Rotations Summary" diagram (was already included in PS13 solutions).
- Final exam due date will be Fri 3/21.
- Based on poll in class today:
- No OH Th 3/13 and Su 3/16.
- Usual OH M 3/17 7-9 pm.
- SG available F 3/14, M 3/17, W 3/19 10-11 am (usual class time) by request. Send email if you want to meet.
- Don't forget to fill out your online course assessments, you should receive email about this.
- PS13 and many late PS's up through PS11 available for pickup.
- Updated anonymous grade and grade histograms posted -- check that we have the right scores for you!
- 2008/03/10
- Updated Lecture 48 (material from 3/7 and 3/10) and lecture
notes posted. You need this
material for PS14 #4. Updated 6:40 pm with factor of 2 correction
in spin-orbit coupling.
- Nominal due date for final exam will be 3/18 -- do you want to delay it until 3/21? Poll will be taken in class, 3/11.
- Corrected error in Lecture 45 (2/29) -- Wigner-Eckart theorem
proof of vanishing of Stark Effect first-order energy shift was wrong.
- 2008/03/07
- Lecture 48 (3/7) and updated lecture notes posted.
- PS12 and many late earlier PS's available for pickup.
- 2008/03/05
- Lecture 47 (3/5) and updated lecture notes posted. Lecture 46 (3/3) has been split into lectures 46 and 47.
- PS14 posted and will be due
on the normal schedule, on 3/11.
Vital Information
Location:
107 Downs
Time: MWF 10:00 am - 11:00 am
Instructor: Prof. Sunil Golwala, 311 Downs, Mail Code 59-33, golwala at caltech.edu
Teaching Assistants:
Time: MWF 10:00 am - 11:00 am
Instructor: Prof. Sunil Golwala, 311 Downs, Mail Code 59-33, golwala at caltech.edu
Teaching Assistants:
Hsin-Hua Lai, hsinhua at caltech.edu
Chan Youn Park, splendid at caltech.edu
Jaewon Song, jaewon at caltech.edu
Sean Tulin, tulin at caltech.edu
Please contact the TAs directly if you would like to make appointments outside of normal office hours.
Office Hours and Contact Information:Chan Youn Park, splendid at caltech.edu
Jaewon Song, jaewon at caltech.edu
Sean Tulin, tulin at caltech.edu
Please contact the TAs directly if you would like to make appointments outside of normal office hours.
Prof. Golwala: M 7-9
pm, 107 Downs.
Additional office hours can be arranged by appointment or by popular demand.
If you need to contact me outside of office hours, please try email first. I am happy to arrange meetings outside of normal office hours, but I am not always available on the spur of the moment. Please include "Ph125" in the subject line of your email -- I get a lot of email, and I want to make sure I see your emails quickly.
Additional office hours can be arranged by appointment or by popular demand.
If you need to contact me outside of office hours, please try email first. I am happy to arrange meetings outside of normal office hours, but I am not always available on the spur of the moment. Please include "Ph125" in the subject line of your email -- I get a lot of email, and I want to make sure I see your emails quickly.
TAs:
Th 6-8 pm 425 Downs/Lauritsen (theory interaction room).
Su 9-11 pm 425 Downs/Lauritsen (theory interaction room).
The TAs will rotate through these office hours.
Let us know if you have trouble getting into Downs; we can move these OH to 107 Downs or to SFL if so desired.
Th 6-8 pm 425 Downs/Lauritsen (theory interaction room).
Su 9-11 pm 425 Downs/Lauritsen (theory interaction room).
The TAs will rotate through these office hours.
Let us know if you have trouble getting into Downs; we can move these OH to 107 Downs or to SFL if so desired.
Feedback:
I greatly appreciate student
feedback; feedback prior to the end-of-term evaluations lets me modify
the class to fit your needs. In
person, by email, by campus mail, whatever you like. If you would
like
to preserve your anonymity, campus mail will usually work. I have
mailboxes on the 3rd floor of Downs near my office and in 61 W.
Bridge.
Ombudspersons: I would also like to have two student ombudspersons for the class. Contact me to volunteer.
Ombudspersons: I would also like to have two student ombudspersons for the class. Contact me to volunteer.
Textbook(s)
- Required: Principles of Quantum Mechanics,
Shankar, available at the bookstore.
- Optional (on 3-hr reserve
at Fairchild Library):
Use these optional texts for alternate explanations or for additional problems or examples. The basic material is always the same, but different authors have different approaches. Find a text you like; different students learn in different ways -- internalizing your own understanding of the material is key to becoming expert in it, so you should follow the approach that best gets you there.
- Comparable to this course
- Griffiths, Introduction to Quantum Mechanics, not quite as advanced as this course.
- Cohen-Tannjoudji et al., Quantum Mechanics, similar to this course, but very axiomatic and long -- I prefer Shankar.
- Gasioriowicz, Quantum Physics, a good book -- I used this as an undergrad and was fairly happy with it. A bit less rigorous than I like, which is why I am using Shankar.
- Liboff, Introductory
Quantum Mechanics, a good book at the right level, but the
typesetting is so similar to the most recent edition of Goldstein as to
cause unnecessary mental trauma.
- Merzbacher, Quantum Mechanics, a classic, writing and text style is also "classic" (dense text, not very many exercises)
- Messiah, Quantum Mechanics, c.f. Merzbacher
- Schiff, Quantum Mechanics,
c.f. Merzbacher
- More advanced than this course
- Landau and Lifshitz, Quantum
Mechanics, similar material to this course, very terse.
- Sakurai, Modern Quantum Mechanics: largely the same material as this course, but probably too terse for the first time through.
- Sakurai, Advanced Quantum
Mechanics: covers second quantization and relativisitic
QM. Only for certified quantum mechanics.
- Special topics (self-explanatory)
- Weissbluth, Atoms and Molecules
- Lecture Notes:
My lecture notes in general follow Shankar and are primarily intended as a distillation for my personal use. It will appear in class that I am working directly from them because I am -- that's why they're called lecture notes! My goals in making them available to you are:
- To provide clarification of points in Shankar that I thought
deserved more or alternate explanation.
- To present additional explanation or material derived from other texts; the references will be provided in the notes.
- To get all the algebra down on the page, correctly, so that I don't get bogged down on the board and so that you don't have to transcribe everything that I write.
I only provide the notes in electronic pdf form, available below. Corrected versions will be posted here, too. The lectures are also broken out separately in the syllabus down below, with individual lecture update dates.
I do not consider myself responsible for providing updated copies of the lecture notes well ahead of class time -- they are being written as the course is being given. They will be posted promptly after class. I suggest that you spend your time in class following the lecture at a conceptual level and noting down for yourself points or derivations that were not clear to you; when you review the posted notes, you may find your questions answered. If not, you are welcome to ask for clarification.
Of course, it is true that the lecture notes may relieve you of the obligation of coming to lecture. I won't claim that there is much said in class that is not in the notes. It's your choice. Some students benefit from being able to receive information aurally and to interact during that process; others prefer to read it off the page. Whatever works for you. Grades are based only on the written work you hand back.
But please do not delude yourself into thinking that, because the lecture notes are available, that you can just skim through it all on the day before a problem set or exam is due and expect to immediately become expert. Learning requires time to mull over concepts in your mind, for your subconscious to work on ideas and problems. If you choose not to come to class, please be disciplined about keeping up with the material in your own study time.
- To provide clarification of points in Shankar that I thought
deserved more or alternate explanation.
Lecture Strategy
I will not cover in lecture every bit
of material
you will be responsible for. There are some topics that are
really better covered by reading than by lecture, and some topics that
are simple enough that they are a waste of lecture time. I can
use the leftover time to do more examples.
Problem Set Policies
The best way to learn physics is by
doing problems. In addition to the regular problem sets, I list below some links to other sources of
problems, some with solutions -- doing problems is the best way to
learn. All these policies are
subject to change when Prof. Cross takes over for Ph125c.
- Problem sets will be posted below,
linked
to the syllabus, usually 1
week before they are due.
- Due date: Tuesday 4 pm at the
box outside my office. No
mercy will be granted
on the due date and time. Remember,
we give partial credit, so the last 10 minutes of work will not make
much difference.
- Late policy: Problem sets will be accepted up to 1 week late at
the due date for the following week's set for
50% credit, and after that not
at all. You may turn in part on-time and part late. Please note on the problem set if it is
being split this way. You do not need to contact me or
the TAs
to turn in a problem set late at 50% credit, or to turn in part on-time
and part late.
- Extensions:
- You may take one
full-credit one-week extension per term. No need to contact us,
just write it on your problem set.
- Otherwise, extensions will be granted for good
reasons -- physical or mental health issues, family emergency,
etc. You must contact me or one of
the TAs before the homework is
due and you must provide some sort of proof (e.g., note from resident
head, health center, counseling center, or Barbara Green). A
heavy amount of other
coursework is not
sufficient reason for an extension (though you may use your free
extension in such circumstances -- so save it until you really need
it!).
- Solution sets will be posted in the
same location when the homework
sets are
due (usually late the same night or the following morning). If
you turn in the problem set late, you may not look at the
solutions until you have turned in your problem set.
- Graded problem sets will be available
roughly 10 days after they are
due, outside my office.
Grading
The course grade will be one-third
homework
sets, one-third midterm, and one-third final.
Collaboration is permitted on homework sets, but each student's solution must be the result of his or her own understanding of the material. No manual xeroxing is allowed. See below for some comments on working in groups.
Use of mathematical software like Mathematica is allowed, but will not be available for exams. Prof. Mabuchi made a very good point when he taught Ph125: It is absolutely essential that you develop a strong intuition for basic calculations involving linear algebra, differential equations, and the like. The only way to develop this intuition is by working lots of problems by hand; skipping this phase of your education is a really bad idea. Be careful how you use such packages.
The midterm and final are not collaborative, though you are welcome to consult your own notes (both in-class and any additional notes you take), Shankar, and my lecture notes (including typo corrections). You may not use other textbooks, the web, any other resources, or any software of any kind.
Grade Distributions and Anonymously Listed Grades
Collaboration is permitted on homework sets, but each student's solution must be the result of his or her own understanding of the material. No manual xeroxing is allowed. See below for some comments on working in groups.
Use of mathematical software like Mathematica is allowed, but will not be available for exams. Prof. Mabuchi made a very good point when he taught Ph125: It is absolutely essential that you develop a strong intuition for basic calculations involving linear algebra, differential equations, and the like. The only way to develop this intuition is by working lots of problems by hand; skipping this phase of your education is a really bad idea. Be careful how you use such packages.
The midterm and final are not collaborative, though you are welcome to consult your own notes (both in-class and any additional notes you take), Shankar, and my lecture notes (including typo corrections). You may not use other textbooks, the web, any other resources, or any software of any kind.
Grade Distributions and Anonymously Listed Grades
Syllabus and Schedule, Lecture Note References, Problem Sets, and Solutions
Boldface:
major topic for day
Normal typeface: specific topics to be covered
Readings in Shankar or the lecture notes are listed.
The standard QM syllabus will take us about halfway through winter term. For the second half of winter term, we have many choices as to what special topics to cover. Please send me your preferences about what you might like to see; some ideas, in order of decreasing instructor expertise:
Up-to-date complete lecture notes
(updated 2008/03/12).Normal typeface: specific topics to be covered
Readings in Shankar or the lecture notes are listed.
The standard QM syllabus will take us about halfway through winter term. For the second half of winter term, we have many choices as to what special topics to cover. Please send me your preferences about what you might like to see; some ideas, in order of decreasing instructor expertise:
- Fermi gas
- Phonons
- Periodic potentials/tunneling resonances/Bloch waves/band
structure
- Bose-Einstein Condensation/Superconductivity
- NMR/Rabi Oscillations/Two-Level Systems
- Second quantization and quantum field theory
- Squeezed states and quantum harmonic oscillators
- EPR/Bell's inequalities
- Quantum computing
- Quantum cryptography
- Quantum entanglement
- Quantum measurement theory
| Homework Due w/b |
Monday Class | Wednesday
Class |
Friday Class |
| Fall, 2007 |
|||
| Oct 1 PS1 posted (posted 2007/10/03) v. 2 posted 2007/10/05 |
Oct 1 Introduction to Course Introduction to Postulates Lecture Notes Mathematical Preliminaries linear vector spaces Shankar 1.1 Lecture 1 |
Oct 3 Mathematical Preliminaries linear vector spaces inner product spaces Shankar 1.1-1.4 Lecture 2 |
Oct 5 Mathematical Preliminaries inner product spaces linear operators Shankar 1.4-1.7 Lecture 3 |
| Oct 8 Problem Set 1 due PS1 solutions posted PS2 posted |
Oct 8 Mathematical Preliminaries eigenvalue problems Shankar 1.8 Lecture 4 (updated 2007/10/18) |
Oct 10 Mathematical Preliminaries eigenvalue problems functions of operators Shankar 1.8-1.9 Lecture 5 (updated 2007/10/12 corrected Eq 3.82 2007/10/15) |
Oct 12 Mathematical Preliminaries calculus with operators infinite-dimensional generalization Shankar 1.9-1.10 Lecture 6 |
| Oct 15 Problem Set 2 due PS2 solutions posted v. 3 posted 2007/10/27 PS3 posted v. 2 posted 2007/10/18 |
Oct 15 Mathematical Preliminaries infinite-dimensional generalization Shankar 1.10 Lecture 7 |
Oct 17 Mathematical Preliminaries infinite-dimensional generalization Shankar 1.10 Lecture 8 |
Oct 19 Mathematical Preliminaries infinite-dimensional generalization Shankar 1.10 Lecture 9 |
| Oct 22 Problem Set 3 due PS3 solutions posted PS4 posted v. 2 posted 2007/10/25 |
Oct 22 Postulates Shankar 4 Lecture 10 |
Oct 24 1D Problems free particle Shankar 5.1 Lecture 11 Updated 2007/11/02 (a couple extra hbars) java applet |
Oct 26 1D Problems particle in a box Shankar 5.2 Lecture 12 |
| Oct 29 Problem Set 4 due PS4 solutions posted midterm posted |
Oct 29 1D Problems particle in a box ct'd: uncertainty relations general points on bound states continuity equation Shankar 5.2-5.3 Lecture 13 |
Oct 31 1D problems step-potential scattering: finding the eigenstates Shankar 5.4 Lecture 14 |
Nov 2 1D problems step-potential scattering: wave-packet evolution Shankar 5.4 Lecture 15 |
| Nov 5 Midterm due midterm solutions posted PS5 posted v. 2 posted 2007/11/10 v. 3 posted 2007/11/11 |
Nov 5 1D problems general theorems Shankar 5.6 Harmonic Oscillator coordinate basis Shankar 7.1-7.3 Lecture 16 |
Nov 7 Harmonic Oscillator coordinate basis ct'd energy basis Shankar 7.3-7.4 Lecture 17 |
Nov 9 Harmonic Oscillator energy basis ct'd energy-coordinate basis correspondence rewriting Postulate 2 Shankar 7.4-7.5 Lecture 18 |
| Nov 12 Problem Set 5 due PS5 solutions posted PS6 posted v. 2 posted 2007/11/14 |
Nov 12 Uncertainty Relations operator uncertainty relations Shankar 9 Lecture 19 |
Nov 14 Uncertainty Relations energy-time uncertainty relation Shankar 9 Multiparticle Systems fundamentals Shankar 10.1-10.2 Lecture 20 |
Nov 16 Multiparticle Systems fundamentals Shankar 10.1-10.2 Lecture 21 |
| Nov 19 Problem Set 6 due PS6 solutions posted PS7 posted v. 2 posted 2007/11/20 v. 3 posted 2007/11/21 v. 4 posted 2007/11/24 |
Nov 19 Multiparticle Systems identical particles Shankar 10.3 Lecture Notes Lecture 22 Updated 2007/11/21 |
Nov 21 Multiparticle Systems identical particles Shankar 10.3 Lecture Notes Lecture 23 |
Nov 23 No class/Thanksgiving |
| Nov 26 Problem Set 7 due TUES NOV 27 4 PM (Note date change) PS7 solutions posted v. 2 posted 2007/12/05 |
Nov 26 Symmetries Shankar 11 Lecture Notes Lecture 24 |
Nov 28 Symmetries Shankar 11 Lecture Notes Lecture 24 |
Nov 30 Symmetries Shankar 11 Lecture Notes Lecture 24 PS8 posted |
| Dec 3 See Dec 7 |
Dec 3 Symmetries Shankar 11 Lecture Notes Lecture 25 updated 2007/12/05 |
Dec 5 Symmetries Shankar 11 Classical Mechanics Classical Limit Shankar 2, 6 Lecture Notes Lecture 26 updated 2007/12/07 |
Dec 7 Classical Mechanics Classical Limit Shankar 2, 6 Lecture Notes Lecture 27 Review for Final Problem Set 8 due Dec 7 PS8 solutions posted Final exam posted on Dec 7 Final Exam due Dec 14 |
| Winter, 2007 |
|||
| Jan 7 |
Jan 7 WKB Approximation Shankar 16.2 Lecture Notes Lecture 28 updated 2007/01/10 |
Jan 9 WKB Approximation Lecture Notes Lecture 29 updated 2007/01/20 |
Jan 11 Variational Method Shankar 16.1 Lecture Notes Lecture 30 updated 2007/01/16 |
| Jan 15 PS9 posted v. 2 posted 2008/01/19 |
Jan 14 Rotations and Coordinate Angular Momentum classical and quantum rotation formalism in 2D Shankar 12.1-12.2 Lecture 31 updated 2007/01/16 Ph106 LN 5.1.1-5.1.3 |
Jan 16 Rotations and Coordinate Angular Momentum quantum formalism in 2D coordinate basis evec-eval problem in 2D classical formalism in 3D quantum formalism in 3D Shankar 12.3-12.4 Lecture 32 Ph106 LN 5.1 |
Jan 18 Rotations and Coordinate Angular Momentum evec-eval problem in 3D: coordinate basis (spherical harmonics) operator method (raising/lowering ops) Shankar 12.5 Lecture 33 |
| Jan 22 Problem Set 9 due PS9 solutions posted PS10 posted |
Jan 21 No class (MLK Holiday) |
Jan 23 Rotations and Coordinate Angular Momentum operators in the |j,m> basis |j,m> basis - coord basis correspondence Shankar 12.5 Lecture 34 |
Jan 25 Rotations and Coordinate Angular Momentum rotationally invariant problems in 3D Shankar 12.6 Lecture 35 updated 2008/03/02 |
| Jan 29 Problem Set 10 due PS10 solutions posted PS11 posted |
Jan 28 Spin Angular Momentum review of tensors in classical mechanics tensor operators in QM Lecture Notes 14.1-14.2 Lecture 36 |
Jan 30 Spin Angular Momentum tensor states in QM Lecture Notes 14.2 Lecture 37 updated 2008/02/11 |
Feb 1 Spin Angular Momentum kinematics and dynamics Shankar 14 Lecture Notes 14.3-14.4 Lecture 38 |
| Feb 5 Problem Set 11 due PS11 solutions posted v. 2 posted 2008/02/08 midterm posted |
Feb 4 Spin Angular Momentum dynamics Shankar 14 Lecture Notes 14.4-14.5 Lecture 39 |
Feb 6 Addition of Angular Momenta basic formalism Shankar 15.1-15.2 Lecture 40 updated 2008/03/02 |
Feb 8 Addition of Angular Momenta basic formalism Shankar 15.1-15.2 Lecture 41 |
| Feb 12 Midterm due midterm solutions posted PS12 posted |
Feb 11 Addition of Angular Momenta spherical tensors states and operators Lecture 42 updated 2008/02/15 |
Feb 13 Addition of Angular Momenta accidental degeneracies Shankar 15.3-15.4 Lecture Notes Lecture 42 updated 2008/02/15 |
Feb 15 Addition of Angular Momenta Wigner-Eckart Theorem representation theory Lecture Notes Lecture 42 updated 2008/02/15 |
| Feb 19 Problem Set 12 due PS12 solutions posted PS13 posted |
Feb 18 No class (President's Day Holiday) |
Feb 20 Time-Independent Perturbation Theory formalism Shankar 17.1 Lecture 43 updated 2008/03/03 |
Feb 22 No class |
| Feb 26 |
Feb 25 Unperturbed Hydrogen Atom READ Shankar 13 (was only summarized in class) Lecture 44 Review of rotations etc., (Lectures 31-42) during evening OH |
Feb 27 Review of rotations etc., cont'd (Lectures 31-42) Rotations Summary diagram |
Feb 29 Perturbed Hydrogen Atom Selection Rules Lecture 43 Stark effect Shankar 17.2 Lecture 45 update 2008/03/10 Problem Set 13 due PS13 solutions posted |
| Mar 4 PS14 posted |
Mar 3 Perturbed Hydrogen Atom degenerate perturbation theory Lecture 43 hydrogen fine structure Shankar 17.3 Lecture 46 updated 2008/03/05 |
Mar 5 Perturbed Hydrogen Atom hydrogen fine structure spectroscopic notation Shankar 17.3 Lecture 47 |
Mar 7 Helium Atom Lecture Notes Lecture 48 updated 2008/03/10 |
| Mar 11 Problem Set 14 due PS14 solutions posted updated 2008/03/14 Final exam posted Final Exam due Mar 21 |
Mar 10 Helium Atom Lecture Notes Lecture 48 |
Mar 12 Multielectron Atoms Hartree-Fock Lecture Notes Lecture 49 Review for Final |
|
Exams
Exam Parameters: All exams will
be 4 hours, to be done in one sitting, but with a total of 30 minutes
of break time allowed. Policies on what materials you may use are
given above.
Midterm, Fall term: All lectures through Oct 19, Shankar Chapter 1, Lecture Notes Section 3.
Exam instructions (1 page): Download these first!
Exam (2 pages): Don't download this until you are ready to take the exam.
Solutions
Comments: The class did quite well on the whole, better than I expected! Median 90%, mean 86%, stdev 13%.
I am happy to see that you have digested the math fundamentals well. This was a very doable exam, so if you got a score below ~90%, you really need to go back and understand where your difficulties are.
The final will be more challenging...
Final, Fall term: All lectures through Dec 5, excluding material on time-reversal transformations.
Exam instructions (1 page): Download these first!
Exam (1 page instructions + 2 pages exam): Don't download this until you are ready to take the exam.
Solutions
Comments: Mean score 68%, median 70%, rms 20%. This exam was 10 points harder than it should have been, but I guess it makes up for the midterm being 10 points too easy. Problem 2 was the one that turned out to be more difficult than I expected. I suppose the issue is that it may not have been obvious how to start it; it turns out to be a "follow your nose" problem, so it's a lesson that, in the absence of anything better to do, just start writing down expansions in terms of eigenstates and see what happens.
Midterm, Winter term: All lectures through Jan 25, Shankar Chapters 12 and 16, Lecture Notes Sections 11-13.
Exam instructions (1 page): Download these first!
Exam (2 pages): Don't download this until you are ready to take the exam.
Solutions
Comments: Mean score 59%, median 62%, rms 20%. I am surprised -- I was afraid this exam would be too easy. Some comments from the graders on specific problems:
Final, Winter term: All lectures through Mar 10, more details on instructions page.
Exam instructions (1 page): Download these first!
Exam (1 page instructions + 2 pages exam): Don't download this until you are ready to take the exam.
Solutions
Comments: Mean score 47%, median 46%, rms 29%. Shocking.
Midterm, Fall term: All lectures through Oct 19, Shankar Chapter 1, Lecture Notes Section 3.
Exam instructions (1 page): Download these first!
Exam (2 pages): Don't download this until you are ready to take the exam.
Solutions
Comments: The class did quite well on the whole, better than I expected! Median 90%, mean 86%, stdev 13%.
I am happy to see that you have digested the math fundamentals well. This was a very doable exam, so if you got a score below ~90%, you really need to go back and understand where your difficulties are.
The final will be more challenging...
Final, Fall term: All lectures through Dec 5, excluding material on time-reversal transformations.
Exam instructions (1 page): Download these first!
Exam (1 page instructions + 2 pages exam): Don't download this until you are ready to take the exam.
Solutions
Comments: Mean score 68%, median 70%, rms 20%. This exam was 10 points harder than it should have been, but I guess it makes up for the midterm being 10 points too easy. Problem 2 was the one that turned out to be more difficult than I expected. I suppose the issue is that it may not have been obvious how to start it; it turns out to be a "follow your nose" problem, so it's a lesson that, in the absence of anything better to do, just start writing down expansions in terms of eigenstates and see what happens.
Midterm, Winter term: All lectures through Jan 25, Shankar Chapters 12 and 16, Lecture Notes Sections 11-13.
Exam instructions (1 page): Download these first!
Exam (2 pages): Don't download this until you are ready to take the exam.
Solutions
Comments: Mean score 59%, median 62%, rms 20%. I am surprised -- I was afraid this exam would be too easy. Some comments from the graders on specific problems:
- It was surprising how many people did the WKB integral only over
the range [0, E/mg] in spite of the specific hint that WKB was invalid
at the origin. There didn't seem to be appreciation of the hint
about using the symmetric potential results.
- The surprise here was that most people got started off on the wrong foot, either trying to use Gram-Schmidt orthogonalization as if the true ground state were known, or assuming there were only two states, etc. The technique for solving the problem was similar to what we had done in class to determine the bound on excited state energies, but with a tweak that made use of the condition < psi1| psi0 > = 0 instead of < psi1 | phi0 > = 0.
- Part (a) seemed to be the difficult part here; admittedly, it requires good understanding about what the raising and lowering operators do, but still surprising. Part (b), which was just a computation, went well.
- Apparently, understanding how the parity operator acts in
spherical coordinates was a problem.
- No comments from grader yet.
Final, Winter term: All lectures through Mar 10, more details on instructions page.
Exam instructions (1 page): Download these first!
Exam (1 page instructions + 2 pages exam): Don't download this until you are ready to take the exam.
Solutions
Comments: Mean score 47%, median 46%, rms 29%. Shocking.
Practice Problems
Here are some links to good reference
for practice problems. Doing problems is the best way to learn!
Comment on Working in Groups:
It is in general a good thing to work
with other students while reading and doing problem sets. You get
to hear different perspectives on the material and frequently your
peers can help you get past obstacles to understanding.
However, you must use group work carefully. If you rely on your colleagues too much, or take a very long time to do the homework sets, you will do poorly in the fixed-time, independent exam environment. Empirically, we observe that students with good exam scores tend to also have done well on homework, but that good homework scores do not predict good exam scores. Exam scores correlate from exam to exam, even on largely independent material. For example, scores from 2004-2005 Ph106ab:
Notice, in particular, the midterm-final correlation for Ph106b, which is remarkable because the exams covered totally disjoint material (mechanics vs. E&M) and were written by two different instructors.
To avoid suffering from this problem, I have two suggestions:
However, you must use group work carefully. If you rely on your colleagues too much, or take a very long time to do the homework sets, you will do poorly in the fixed-time, independent exam environment. Empirically, we observe that students with good exam scores tend to also have done well on homework, but that good homework scores do not predict good exam scores. Exam scores correlate from exam to exam, even on largely independent material. For example, scores from 2004-2005 Ph106ab:
Notice, in particular, the midterm-final correlation for Ph106b, which is remarkable because the exams covered totally disjoint material (mechanics vs. E&M) and were written by two different instructors.
To avoid suffering from this problem, I have two suggestions:
- Talk to your peers, in particular peers outside of your usual
workgroup, to find out how long they are spending on problem
sets. If you find you are spending much more time, figure out
why! Do you need to spend more time understanding the material
before diving in to problem sets? Do you jump to an incorrect
solution method too quickly? Are you getting bogged down in
algebra? Consult me or the TAs too.
- While working in groups can be helpful, you have to be careful to
remain sufficiently independent that you can solve problems on your
own! My suggestion is to go over the material and examples in
groups, but try to work the problems by yourself, using help from
others as a last resort. If you find yourself helping one of your
peers, don't just explain how to do the problem; try to help him find
his way to the solution himself.
This is not just an arbitrary classroom
exercise. In research, one is always under schedule pressure --
because one only has a fixed number of nights at an observatory,
because there are funding deadlines, because there are competing groups
doing similar work. It is critical to learn how to cut through
irrelevant or unimportant information and get to results in a timely
fashion.
Announcements Archive
- 2008/03/03
- Tonight's OH canceled:
not enough response. I can be available for appointments this
week, contact me if you want to meet, or go to Thurs night OH.
- Lecture 46, updated Lecture 43 (deg. pert. theory), and updated lecture notes posted
- Change in syllabus: not
enough time left to do time-dependent pert. theory, Prof. Cross will do
it next term. We will finish up with multielectron atoms, Hartree-Fock
approx,
- 2008/03/02
- PS13 solutions full version posted.
- Corrections to lectures 35 and 40 posted based on above.
- 2008/02/29
- Two questions:
- Do you want OH on Sunday or Monday night? No PS due, but we would be happy to have them to continue to help you understand the material. Please email us if you do plan to attend.
- May I delay the PS14 due date until W Mar 12 or Th Mar
13? I am running out of time and will not be able to complete
Radiation until Mon Mar 10, and I want to give you a reasonable amount
of time to complete the HW if I include problems on this topic.
- Lecture 45 (2/29), updated Lecture 43 (2/20), updated lecture notes posted. As I derive more of the formalism of time-independent perturbation theory, I am posting it as part of Lecture 43 because, conceptually, that is where it belongs. Last update should be on Monday Mar 3.
- Syllabus updated.
- 2008/02/28
- Updated answers to questions; not all complete, but most of
them.
- 2008/02/27
- Have begun to answer questions sent in by email for PS13 (1/3
done, I think). They are being compiled in the PS13 solutions,
see below. Watch out for
typos --
not carefully reviewed yet. I hope to get this done by late
afternoon Thursday to help you complete the remainder of PS13.
- 2008/02/26
- Lecture 44 (2/25), updated Lecture 43 (2/20), and updated
lecture notes posted.
- 2008/02/25
- PS13 due date delayed until
Fri, Feb 29, 4 pm. It became clear from tonight's office
hour session that a large fraction of the class would benefit.
Apologies to those who have already turned in PS13 or were planning to
turn it in on time; while perhaps unfair to you, it seemed that
delaying the due date would, on the whole, do the most good. If
you have already deposited PS13 in the IN box, you may recover it and
work on it further if you would like.
- Lecture 43 (2/20) and updated lecture notes posted.
- Since there are only two substantive problems in this week's
set, there will be a lot of time for discussion at tonight's office
hours. Please bring questions! I can start early, 6 pm, if
there is interest.
- 2008/02/21
- PS13 posted. Apologies for the tardiness. Problem 1 requires an email to be sent by Monday night, please look at it early.
- PS12 solutions posted.
- Lecture 43 (2/20) and updated lecture notes will be posted today or Friday.
- 2008/02/15
- Midterm exams available for pickup. See commentary below.
- Grade histograms for midterm also available, see below.
- Nominally final version of Lecture 42 (2/11-2/15) and updated lecture notes posted.
- See notes below about class and office hours on Monday Feb 20.
- I am getting the
distinct feeling that no one understands the material from
2/11-2/15. I am happy to hold an informal summary/Q&A session
if there is interest (maybe the first 30 minutes of Monday's office
hour?). Let me know by Monday noon if you are interested.
- 2008/02/13
- Lecture 42 (2/11-2/13) and updated lecture notes posted. Lecture 42 will be updated again on Friday to contain the complete material on spherical tensor states and operators and applications thereof.
- READ Shankar Ch 13 on the unperturbed hydrogen atom by Feb 20. It is straightforward, I will only summarize the results from it in class.
- There will be no class on Feb 22. Use the time to catch up...
- Midterm solutions posted. We hope to have midterms available for pickup on Friday afternoon.
- PS12 posted.
- There will be office
hours on Monday Feb 18 even though it is a holiday.
- 2008/02/11
- Lecture 42 (2/11), updated
lecture 37 (1/30), and updated lecture notes posted. When
considering spherical tensor operators, it turns out to be better to
define tensor states in terms of an active transformation, so I revised
the definition given in lecture 37.
- 2008/02/08
- Lecture 41 (2/8) and updated lecture notes posted.
- Error in PS11 #5 solutions corrected (calculation of probabilities was wrong).
- PS10 available for pickup (2:15 pm).
- No office hours Monday night
(2/11) unless I receive specific requests. It's probably
too late to be of any use...
- 2008/02/06
- Lecture 40 (2/6) and updated lecture notes posted.
- PS11 solutions posted.
- Midterm exam posted below.
- PS9 available for pickup. There is 1 set without a name -- please claim it.
- PS10 will be available for pickup on Friday (hopefully...)
- 2008/02/04
- Lecture 39 (2/4) and updated lecture notes posted.
- 2008/02/01
- Lecture 38 (2/1) and updated lecture notes posted.
- Midterm will be available Tues or Wed of next week. It
will cover material through 1/25 (Lecture 35).
- 2008/01/30
- Lectures 36 and 37 (1/28 and 1/30) and updated lecture notes posted.
- I am deviating significantly from Shankar in my discussion of spin and addition of angular momentum. Don't feel too obligated to read ahead; you may find it more productive to go back and skim Shankar after you have attended lecture and gone over the lecture notes.
- PS11 posted.
- PS10 solutions posted.
- 2008/01/27
- Lecture 35 (1/25) and updated lecture notes posted.
- 2008/01/23
- PS9 solutions posted
- Lecture 34 (1/23) and updated lecture notes posted.
- 2008/01/22
- Syllabus updated.
- PS10 posted.
- 2008/01/20
- Updated lecture notes 29 (WKB bound states) posted -- some minor typos in Eqns 11.64 and 11.65 fixed, might be confusing for PS9 if you didn't catch them. Should have been evident from the units.
- PS9 #2 typo: if P = 1021T, then tau = 1/P = 1021/T is incorrect, it should be tau = 1/P = 10-21/T.
- PS9 #4 hint: you can check
your result by taking the limit of the anharmonic term becoming
small.
Be sure to construct a reasonable dimensionless criterion for what is
meant by small.
- 2008/01/19
- PS9 v. 2 posted:
important typos/algebraic errors in #1 fixed, other minor typos and
clarificaions
- Office hours: sorry about the confusion this week. We will tentatively have TA office hours both Th 6-8 pm and Su 9-11 pm, and instructor office hours M 7-9 pm. If turnout at one or the other TA office hour is low after 2 weeks, it will be canceled in favor of scheduled appointments.
- Lecture 33 (1/18) and updated lecture notes posted.
- 2008/01/16
- PS9 posted.
- Lecture 32 (1/16), updated lectures 30 and 31 (1/11 and 1/14)
-- minor modifications, and updated lecture notes posted.
- 2008/01/14
- PS due day will be changed to
Tuesday 4 pm for this term. (A poll taken during class
indicated no major objections to the change, let me know if you have
any.) Instructor office hours
will be changed to M 7:00-9:00. TA office hours will also be
changed, check here later.
- Lecture 31 (1/14) and updated lecture notes posted.
- 2008/01/12
- Lecture 30 (1/11) and updated lecture notes posted.
- 2008/01/11
- Lccture 29 (1/9) and updated notes posted, minor updates to
Lecture 28 made.
- 2008/01/09
- Welcome to winter term. No significant changes.
- Lecture 28 (1/7) and updated notes posted.
- The first problem set of winter term will be posted next week.
- 2007/12/18
- Updated anonymous grades and grade histograms posted. If
you have contacted me about grade errors after last Wednesday, Dec 12,
your corrections have probably not been put in yet -- I will do them
Tuesday afternoon, Dec 18. Updated
3:50 pm.
- Final exams now available for pickup.
- 2007/12/17
- Final exam solutions posted. Final exams and final grades available in the next day or two.
- 2007/12/12
- There is a PS6 with no name on it in the out box. Please email me if it is yours, otherwise you will receive no credit for this problem set.
- PS8 available for pickup. A number of students answered Problem 3 by providing a necessary but not sufficient condition for P X2 P = X1. Hopefully, you have checked the online solutions and can be sure you understand this for the final.
- Updated anonymous grade
sheet posted -- Check for clerical
errors. Grades will be submitted early next week, it would be
best to make corrections now. Late PS8 may not be included yet.
- 2007/12/11
- PS6 now available for pickup.
- 2007/12/08
- Final exam posted.
- PS8 solutions posted.
- 2007/12/07
- PS5 and PS7 available for pickup, PS6 today or Monday sometime
- I will be available in my office or 107 Downs during normal class hours on M Dec 10 and W Dec 12.
- There will be no Thursday night office hours except by specific request.
- Final will be available late Friday night or early Saturday.
- Updated Lectures 26 and 27 and lecture notes posted.
- 2007/12/05
- Corrections to eqns 63, 66-68
in PS7 sols posted, important for PS8.
- Lecture 26 and updated lecture notes posted. Also,
updated Lecture 25.
- If you are going to use your
free extension on PS8, please turn it in by noon Wednesday Dec 12 --
the TA who will grade PS8 is going to be leaving town on Thursday Dec
13. You will forfeit PS8 if it is not turned in by Wednesday noon.
- Course evaluations will be handed out on Friday -- please come to fill one out, or pick up one from the envelope near the homework boxes at my office.
- Updated anonymous grades and grade histograms (through PS5)
posted.
- 2007/12/03
- Lecture 25 and updated lecture notes posted.
- 2007/11/30
- Lecture 24 (combined for MWF of this week) and updated lecture notes posted.
- PS7 solutions posted.
- PS8 posted. Due Fri Dec
7 4 pm.
- Office hours for w/b Dec 3:
- Golwala: Weds 7:30-9:30 pm, usual place
- TAs: Thurs 6-8 pm, usual place
- 2007/11/24
- PS7 updated yet again, v.
4. Turns out that Problem 5 was correct, see the revised PS for
details.
- 2007/11/21
- Updated lectures 22 and 23 and lecture notes posted.
- PS7 updated again, v. 3.
- 2007/11/20
- PS6 solutions and PS7 posted.
- Note: PS7 already revised,
look for v. 2
- 2007/11/19
- Lecture 22 and updated lecture notes posted.
- PS7 will be due one day later than normal, Tuesday Nov 27 4 pm
- No office hours Thursday Nov 22
- Sunday office hours will be
moved to Monday Nov 26, 7:30-9:30 pm.
- 2007/11/16
- Lectures 20, 21 and updated lecture notes posted.
- PS5 solutions posted (finally!)
- 2007/11/14
- v. 2 of PS6 posted with minor corrections to Problem 2.
- PS5 solutions and 11/14 will not be posted for another day or
so.
- 2007/11/13
- PS6 posted.
- PS5 sols delayed, will be posted late Tuesday or Wednesday.
- Anonymous grade sheet posted -- check for clerical errors!
- 2007/11/12
- Lecture 19 and updated lecture notes posted.
- 2007/11/11
- Important errors corrected in
PS5 Problem (5b). See updated problem set below (v. 3). Had
mistakenly
written k_1 and k_2 as if the well were at -V_0 and the potential was zero
elsewhere, instead of what is given, where the well is at 0 and the
potential is V_0
elsewhere. This changes Equations 8-14. Apologies to
anyone who has been banging his or her head against a a wall trying to
get it to work out. I think this is a minor enough change that
the due date for the problem set should still be ok, but send me email
if you feel otherwise.
- 2007/11/10
- PS5 version 2 posted --
final transmission probability result provided for you to check
against, more guidance given on plotting.
- Lecture 18 and updated lecture notes posted. Please read the section on calculating
[X,P] -- I made some errors in the delta function manipulations on the
board, they have been corrected in the notes. I will go over this
again on Monday.
- 2007/11/09
- PS4 and late PS3 available for pickup.
- Midterms available for pickup.
Grade distributions to be posted over the weekend. We can discuss
on Monday in class, so take a look over the weekend and bring your
questions to class on Monday.
- 2007/11/07
- Lecture 17 and updated notes posted.
- 2007/11/05
- Lecture 16 and update notes posted.
- Midterm exam solutions posted.
- PS5 posted.
- 2007/11/02
- PS3 available for pickup.
- Poll in class today favored office hours today instead of Sunday night. OH will be Fri 4 - 5:30, 311 Downs or 107 Downs depending on attendance. No Sunday OH this week.
- Lecture 15 and update notes posted.
- A couple typos (extra hbars) in Lecture 11 fixed.
- 2007/11/01
- Is there interest in moving
the Sunday office hours to Friday this week? Since
questions this week will be directed at understanding previous
material, not questions on the exam itself, it seems like it would be
helpful to move the Sunday office hour to Friday afternoon or
evening. Let me know your opinions. I will take a poll
during Friday's class. Saturday and Sunday daytime are not
possible. though Saturday night 9-11 pm is -- what better way to spend
a Saturday night?
- 2007/10/31
- Lecture 14 and updated notes posted.
- Midterm exam posted, see below.
- PS2 has been available in the out boxes since last week.
PS3 will be available by the end of this week. PS4 will not be available -- if you did not
keep a copy of yours, you may ask the TAs for it and make a copy
yourself.
- 2007/10/30
- Lecture 13 and updated notes posted.
- PS4 solutions posted.
- List of material to be covered
on midterm posted. Midterm will be posted W evening after TAs
review it.
- 2007/10/27
- Poll on 10/26 gave ~50/50
split for/against delaying the midterm. Will leave midterm date
unchanged, midterm to be posted on M or Tu.
- Updated notes and Lecture 12 posted.
- Minor correction to PS2 solution posted.
- 2007/10/25
- PS4 v. 2 posted: clarifications and hints on Problems 1, 3, 4.
- 2007/10/24
- Updated lecture notes and Lecture 11 posted.
- QUESTION: Do you want to have the midterm handed out Oct 29 and have only math content, or delay it one week and include 1D problems? Send me email, I will take a poll on Fri Oc 26.
- 2007/10/23
- PS4 posted.
- 2007/10/22
- Updated notes and Lecture 10 posted.
- PS2 solutions corrected.
- PS3 solutions posted.
- 2007/10/21
- Updated notes and Lecture 9 posted.
- 2007/10/18
- Updated PS3 posted --
corrected a couple typos and omissions.
- Update notes and lecture 8 posted.
- Minor tweaks to last slide of Lecture 4 posted -- may be helpful to those still having trouble with unitary transformations.
- 2007/10/16
- PS3 posted.
- 2007/10/15
- Updated notes and Lecture 7 posted. I will go over the material on derivatives of the delta function on Wednesday.
- Correction to Eq 3.82 in Lecture 5 -- new version posted.
- PS2 solutions posted.
- The math is really dragging out... one more lecture only, hopefully!
- 2007/10/12
- Lecture 6 posted.
- Lecture 5 revised slightly: just moved some material from
lecture 6 into lecture 5 because it makes more sense there. No
new or corrected content.
- Lecture 4 revised: clarified situation about how unitary
diagonalization ops are defined. Reread the last 2-3 slides.
- 2007/10/10
- Lecture 5 notes posted. Will repeat end-of-class material on differentiation of ops on Friday and post those lecture notes then.
- PS DUE TIME CHANGED TO 4 PM, so
you don't get locked out of the building.
- 2007/10/08
- Lecture 4 notes posted. Formatting of previous lectures
modified, no change in content.
- PS1 solutions posted.
- PS2 posted.
- 2007/10/07
- A number of students have found (physically uninteresting)
counterexamples to the theorems to be proven in Problem 1. We
will
give full credit either to solutions along the lines expected or to
counterexamples. There will be a discussion in the solutions.
- 2007/10/05
- Lecture 3 and updated notes posted.
- Clarifications on PS1 problem 1 posted -- see updated problem set below in the syllabus.
- Revised syllabus posted. May yet stretch out further...
- 2007/10/04
- Lecture 2 and updated notes posted.
- Lectures are going slower than I expected; much material on PS1 will not be covered until Fri Oct 5. I think this should be ok, it's easy material. I will correct this for future weeks: aim is to have material on PS appear no later than W of week before it is due.
- Office hours and problem set due dates decided and posted. First OH this Thursday 6 pm.
- Syllabus being revised (stretched out).
- 2007/10/03 Minor corrections to first lecture posted. PS1
posted.
- 2007/10/02 Notes for first lecture posted.
- 2007/09/24 First version of web page posted. Not complete yet.