**Physics 302- Advanced Quantum Mechanics - 2010**

**Walter Smith**

**Course information and syllabus**

**A brief caveat**

You should expect
this to be a challenging course. Quantum mechanics at this level is quite
formal and mathematical, although every effort will be made to maintain contact
with reality. We also need to move fairly quickly to cover the canonical
content of the course. I have tried to structure the course to encourage
everyone to stay up-to-date and engaged. (In other words, you *should expect to work very hard.*) Most
importantly, however, quantum mechanics is the crowning glory of physics; you
will find it enormously satisfying and even enjoyable to have made a serious
start on mastering it.

**Course organization**

__Instructor__: Walter Smith Bryn Mawr office: Park 344 Haverford office: KINSC L110

896-1332 (office), 896-1565 (home)

Office hours at BMC: Mon 9:00-10:00, Tues 10:30-11:30, Wed 9:00-10:00,

Thurs 10:30-11:30 & 1:00-2:30

Fri 9:00-10:00

Office hours at HC: Tues 2:00-3:00, Wed 10:30-11:30,

Thurs 3:00-4:30

Fri 10:30-11:30, 1:30-2:30

__Location and times__:

· Lecture – TT 11:30-1:00 in Park 337. Attendance is expected.

· Recitation TBA. Attendance is expected.

__Textbook__:

· John S. Townsend, *A Modern
Approach to Quantum Mechanics*

__Other texts that
might be helpful if Townsend is not clear__:

· Richard L. Liboff, *Introductory
Quantum Mechanics, *2nd Ed.

· David S. Saxon, *Elementary
quantum mechanics;*

· P.J.E. Peebles, *Quantum
Mechanics;*

·A. P. French and E. F. Taylor, *An
Introduction to Quantum Physics. *

**Assignments:**

¨
Written work will be assigned each Friday, to be
due the following Friday __at 10:00 am__. There will be two portions to each
assignment.

·
Group problems: For these problems, you are
encouraged to work together in small groups, of no more than 5 people, * after attempting each problem on your
own*. Make sure that you are
contributing to the group effort.

·
Individual assignment: other exercises will be
assigned for all students to work individually. __No collaboration is allowed
on these problems__. You may consult
with any textbooks you like, and with the instructor, but not with any other
human.

· It is important that you write your answers to the assignments in a way which is easily legible and comprehensible. A liberal arts college is supposed to teach you to communicate well; this includes physics problems. Frequently, you will need to add a few words of text to explain what you’re doing, although often the equations can speak for themselves, so long as you lay them out clearly, using arrows, equation numbers, etc. as needed. For many of you, this means you may need to recopy some problems once you’ve figured out the correct way to do them.

¨ Independent project:

· In addition to the relatively wide knowledge of quantum mechanics that you will acquire through the lectures, reading, and problem sets, it is important and satisfying to explore one aspect in greater depth. After spring break, you will begin work on this project. You may select from a list of suggestions or come up with your own project, subject to approval by the instructor. Most projects will culminate in a paper (about 10 pages) or computer program and accompanying documentation. Towards the end of the semester, the number of regular assigned problems will be decreased somewhat to allow more time for your project.

__Tests__:

· There will be 2 mid-term examinations (see detailed syllabus for coverage and dates) and a cumulative final exam.

· The exams will be timed, closed-book, take-home tests.

__Grading procedures
for specific elements of the course__:

· Your course grade will be computed using the following weighting:

Final exam 25%

Homework 32%

Independent project 15%

•
Written exercises--** We will use a
two-pass procedure for handling problem sets – please read carefully!** ** Please
use regular pencil or black ink for your problem sets!!** After you turn in a problem set, it will be
graded using red ink. Half of the grade
for the homework will be based on this first grading pass.

Your paper will then
be turned back to you **the following
Monday morning**, along with “skeleton” solutions. (These are not complete written-out versions
of the problems, but rather guidelines and waypoints to help you along.) At this point, consulting the skeleton solutions
as needed, **using blue ink or blue
pencil,** and writing on the same paper you originally turned in, you will
complete any problems which you were unable to do at first, and write out
complete corrections to problems which you did incorrectly. The goals of doing the grading this way are
to ensure that you understand each problem fully, and also to give you a
“second chance” on problems that you muff.
You will then turn in your revised problem set on the following Monday
in class. Your revised assignment will
then be re-graded (using green ink for grading), and assigned the remaining 50%
of the grade. In principle, everyone
should have a perfect revised version, since you may consult the skeleton
solutions as needed in preparing this.

**To make this whole scheme work, it is essential that you leave
space on your problem set to write in corrections. **You may wish to leave space at the bottom
of each page, or to use the back of the preceding page.

There will be no rewrite on the final assignment, since it will be due on the last day of classes.

**You will be graded on the presentation and comprehensibility of
your assignments. **This does

•
Exams--understanding is the key. Partial
credit will be given for sensible efforts even without a completely correct
answer. We will also use a two-pass
system for the two mid-term exams, with 60% of the weighting from the first
pass and 40% from the second pass. The
first pass will be closed book and timed, while the second pass will be open
book and untimed. (You are not allowed
to consult any human other than me for the second pass.) The final exam will be one pass only.

•
For weekly homeworks, you are permitted __two 1-week extensions (either on a
first pass or on a second pass) without any penalty__ during the semester
when you are stressed out with work.
Just turn in a sheet of paper indicating that you are giving yourself a
"free extension." The two
extensions must be used for separate problem sets; they cannot be combined to
get a two-week extension on one problem set.

If you take an extension on the
first pass, you automatically receive a one-week extension on the second pass
as well, without this counting as your second free extension. You may not consult the skeleton solutions on
your first pass, but must wait for the second pass (just as if you had not
taken the extension). Also, you may not
consult the complete solutions until after you have turned in the second pass.

Save these extensions for when
you really need them. I will only grant
additional extensions for truly grave cases, such as a death in the family or
severe illness; such extensions must be asked for __in advance.__ Other than these extensions, work turned in
late will not be graded.

•
Exams must be turned in not later than the stated times, except by __prior__
agreement.

We value Bryn Mawr’s honor code for the integrity it fosters and the pedagogical flexibility it affords. The important guiding principle of academic honesty is that you must never represent the work of others as your own. The following guidelines should govern your behavior in the course; please request clarification if you find yourself in any doubtful situations.

• You may seek assistance from
the instructor or from your fellow students in doing the weekly assigned
exercises (except for “individual problems”) but *only after attempting each problem yourself*. (Discussion *without* prior effort, except to clarify what the question is
asking, is not permitted.) You may work together with other
members of the class on these assignments and this is often quite beneficial. For your own good, avoid situations in which
you are either contributing either too much or too little to such
collaborations. Do not work in groups of
more than five people; three or four is usually ideal. __Just copying someone else's work is clearly
a representation of another student's work as your own and is a violation of
the Code__.

You may consult with the
isntructor about any problem (including individual problems), but again only
after attempting it yourself.

Your textbook gives the answers
for some of the exercises. These are
given so that you will know if you have done a problem correctly. It is not sound learning procedure to try to
work backwards from given answers, but doing so is not a violation of the honor
code.

•
Solutions to the written exercises will be made available on the due date for
the second pass. If you have taken an
extension, you are not allowed to consult the solutions until you’ve turned in
your second pass.

•
__The take-home exams must be entirely your own work__. Detailed instructions will be given on the
exams themselves and discussed in advance.
You will be allowed to use a page of notes prepared in advance, and a
calculator, but no other materials. No
collaboration of any sort is allowed once you start an exam. The allowed time (a single contiguous block)
must be strictly observed.

•
I will be re-using some materials from previous years. Therefore, you are not allowed to look at
materials from previous years. I will
provide plenty of practice questions to help you prepare for the exams.

You may need to improve your study habits in order to do well in this course. The following suggestions are based on the experience of previous students:

*Review*
your class notes between lectures, and come prepared to ask
questions. *Annotate* your class notes as you read them.

*Stay up to date* on the reading; preferably read
the assigned material *twice*; for
example, once before the relevant lecture, and once after.

*Read with pen in hand* to work out things described only
briefly in the text or lecture. Ask
yourself "what is the main point of each section", and** ***answer*
the question.

When
you take notes in class, *don't just write
down equations*! Qualitative
information is often essential!

Don't
spend more than 1 hour on a single homework problem. Show clearly where you're stumped and just
move on. Don't feel badly if this
happens occasionally, or worry about the effect on your grade. Consistency in doing the homework is more
important.

**You need to allocate about 9 hours
for study and homework per week **(plus
class time).

Do
stop in to see the instructor if you have questions or suggestions.

When
you’re studying for an exam, review the *solutions* to problems and previous exams.

Remember
that if the material is a new or unfamiliar for you, learning will take time,
just as learning a new language takes time
Try not to become discouraged if the going is rough at times, and don't
prejudge your ability to master the material.
Generations of students have done it before you. There is no magic method of presenting the
material that we can use to make it easy.

Students
who think they may need accommodations in this course because of the impact of
a disability are encouraged to meet with the instructor privately early in the
semester. Early contact will help to avoid unnecessary inconvenience and
delays.

Exam 1 will be
distributed 2/19 and due 2/26; Exam 2 will be distributed 3/26 and due 4/2. The
final exam will be held during finals week.
(!) **Note that the amount of
new material covered on the second exam is greater than the first exam.** Plan your study time accordingly! (The weights assigned to these exams have
been adjusted accordingly.)

**Assignment
#1**

Due: Friday, 29 January at 10:00 am.

Reading: Chapter 1 of Townsend

**Group
problems:**

1.3
Ans.to part c: _{} (Your answer will
include a factor of _{}. It is conventional
to choose d = 0.)

1.4
Ans. for the probability of finding _{}

1.5
Ans. for probability of finding_{}

1.6

1.7

**Individual-problem:
**1.8