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Quantum mechanics is absurd! It offers a recipe (a highly mathematical recipe) for finding incredibly accurate answers to problems, yet there is nothing in our common experience that allows us to grasp what is "really" happening. In this course we will work our way through the recipes and try to find meaning in the weirdness. We will have to do some math, but we will make extensive use of computer based mathematical systems to keep as much drudgery out of our effort as possible. I am completely convinced that the only way you learn quantum mechanics is by doing quantum mechanics. Therefore we will do it. We will do lots of problems. To be able to get a grip on this subject is very rewarding. Obtaining that grip is the aim of the course.
The second practical exam of the semester is due on Monday, Nov 24, by 4:00 PM. It will be the library for you to take when ready by Wednesday. 0547 18/xi/08 Answers to DP through 59 and OP through 59 are posted in the Problem Set Answers Table below. Answers to the second conceptual exam are also posted below. 1130 20/xi/08 Daily problems for Friday are 61 and 62. Other problems to 62. 1128 20/xi/08 The Grade Query page is now up to date, through the second conceptual exam. 1142 20/xi/08
Robert Linck
Office, Sabin-Reed 429
Phone, X3836
Email, rlinck(at)email.smith.edu
Office Hours, Tu, 8-11; Th 10-12; 1-3; F, 1-3; or by appointment.
| Item | Link |
|---|---|
| Answers to Problem Set 1 | DP 1-10 |
| Answers to Other Problems | OP 1-7 |
| Mathematica Notebook for | Wed, 9/17 |
| Answers to Daily Problems | DP 11-24 |
| Answers to Other Problems | OP 8-23 |
| Notebook for | P.O.P. |
| Notebook for | V potential |
| Notebook for | harmonic oscillator |
| Notebook for | Potential barrier |
| Answers to Conceptual Quiz | Number One |
| Answers to Practical Quiz | Number One |
| Answers to Conceptual Quiz | Number Two |
| Answers to Practical Quiz | Number Two |
| Answers to Daily Problems | 25-39 |
| Answers to Other Problems | 24-35 |
| Answers to Conceptual Exam | Number One |
| Notebook for | Legendre Polynomial Solutions for Rigid Rotor |
| Notebook for | Spherical Harmonics Visualization |
| Notebook for | Review of Practical Exam One Problems |
| Answers to Daily Problems | 40-54 |
| Answers to Other Problems | 36-51 |
| Answers to Practical Exam | Number One |
| Notebook for | Laguerre Polynomial Solutions for radial part of H atom |
| Notebook for | Perturbation Theory of Parve on Pole |
| Notebook for | Matrix Manipulation |
| Notebook for | Two Dimensional Perturbation Theory |
| Notebook for | Three Dimensional Perturbation Theory |
| Notebook for | Variational Method |
| Notebook for | Wednesday, Nov 12 lecture |
| Answers to Daily Problems | 55-59 |
| Answers to Other Problems | 52-59 |
| Answers to Conceptual Exam | Number Two |
Purpose. This course develops the methods to use quantum mechanics to derive the expected answers to problems involving small things--like electrons and atoms--the things with which chemists are always dealing. We will start with some simple (unreal but useful) one dimensional problems, work on the harmonic oscillator, learn the postulates that govern quantum mechanics, move on to an actual atom, then deal with the subjects necessary to handle multi-electron atoms. This course is of necessity highly mathematical. We will swim in equations throughout the course, trying at all times to keep head above water, to keep our sense of what we really have buried in all that math. We will do some limited amount of math "by hand," but a large part of the exercises are much more easily done by computer based mathematical techniques. This is good because we are interested in the answers to the problems, not the math getting us there.
Meetings. The course is scheduled to meet three times a week, MWF, 0830-0950.
Learning. I have been to a number of workshops over the years that stress that learning is most effective when students are actively engaged. I believe this. I also believe, based on my own experience, that the only way you learn anything about quantum mechanics is by doing it. Accordingly, this course will have assigned problems nearly every class session. These will be graded (at the least in an effort expended sense), either by a peer grading system, or by the instructor, and will compromise a reasonable portion of your grade. You are responsible for doing the assigned problems before each class. We will spend a reasonable portion of class time on problems. We will discuss them together, talk about the merits of a given answer, accept or reject it, improve upon it, refine it, learn from the effort. That is, we will sit around in class as a community of scholars and talk about methods in quantum chemistry. I encourage you to establish some groups which meet regularly to work on problems--and you will need to meet near a computer for most of those problems. This activity will require you to spend time before each class doing problems; I would estimate between one and three hours will be required. That is a reasonable fraction of the 12 hours per week that you are expected (and will probably need) to spend on this class. I expect this class will be intensive. But by the same token, you will learn a tremendous amount: by the end of the first month you will understand how small particles can tunnel through barriers and be able to predict the probability that they will do so--which is all that quantum mechanics can ever say about anything. After six weeks, you will see how by using the nonsensical operators called a+ and a- you will be able to find the allowed energy levels of an oscillator, and so on.
Text. I had a great deal of trouble finding a text for this course. When preparing the material, I used a set of fifteen books, copyrighted between 1930 and 2006, consulting almost all of them on each subject. No one of those books had everything that I wanted. No one of those books explained everything clearly. But from the collection, some sort of sense emerged. As a pure compromise, I chose for a text Quantum Mechanics, by Robert Scherrer, which is available in the bookstore. It treats most subjects we will do, just not always as clearly (or completely) as some other book might treat them.
Exams. There are two quizzes, two exams, and a final scheduled for this course (see the schedule below for dates). Each of these will be in two parts, a conceptual and a practical. The conceptual part will be the usual type of examination in which you will be asked to answer questions without the benefit of notes or texts. This part will not stress the memorization of equations, but rather will try to test your knowledge of the general principles and consequences of quantum mechanics. The practical part will be an examination in which you will be allowed to use any material you wish (notes, texts, etc), including a computer to do fancy math (such as integrations). In this second part you will be expected to produce the right equation for the right situation, either from your memory or by looking it up. (Of course, having to look everything up will be quite time consuming if you are not prepared for the exam!) I will arrange so that all of these assessments are available to you during a period of time so that you may take them when you desire. Both kinds of exams will have time limits imposed.
| Topic | Daily | Other |
|---|---|---|
| Mathematica | DP 1-2 | --- |
| Classic Probability | DP 3-6 | --- |
| Classic Waves | DP 7-10 | OP1-OP3 |
| Functions and Normalization | DP 6-12 | OP4-OP8 |
| Parve on a Pole | DP 13-18 | OP9-OP14 |
| Modified P.O.P. Problems | --- | OP15-OP19 |
| Free Particles, Wells, Walls | DP 19-21 | ---- |
| Harmonic Oscillator-Brute Force | DP 22-25 | OP20-OP24 |
| The Postulates | DP 26-31 | --- |
| Hermitian Operators | ---- | OP25 |
| Ladder Operators for H.O. | DP 32 | OP26-30 |
| Rigid Rotator | DP 34-37 | OP31-OP33 |
| Angular Momentum | DP 38-44 | OP33-39 |
| H Atom Radial Functions | DP 45-50 | OP39-44 |
| Non-Degenerate Perturbation Theory | DP 50-52 | OP44-48 |
| Degenerate Perturbation Theory | DP 53-55 | OP49-OP53 |
| The Variation Theorem | DP 56-57 | OP54-OP55 |
| More Variation: Huckel MO's | DP 58 | OP56-OP59 |
| Intrinsic Angular Momentum | DP 59-62 | OP60-OP62 |
Grading in this course reflects the importance I place on collaborative learning, working on the problems before class, and contributing to our classroom discussion. Grading will be based on 1000 points, distributed as indicated in the table.
| Quizzes (2) | 150 points |
| Exams | 250 points |
| Final Exam | 300 points |
| Discussion and Problem Sets | 300 points |
Your letter grade in the course will depend on the number of points out of the thousand available that you obtain as follows:
| A | >80% of points |
| B | >65% of points |
| C | >45% of points |
| D | >40% of points |
(Plus and minus attachments to these letters will occur near the respective limits of the ranges.)
The schedule of examinations and quizzes is given below. Permission to postpone an examination or quiz will not be given except in exceptional circumstances.
| First Day of Class | 5 Sept |
| Conceptual Quiz One Due | 22 Sept |
| Practical Quiz One Due | 29 Sept |
| Conceptual Quiz Two Due | 6 Oct |
| Practical Quiz Two Due | 10 Oct |
| Fall Break | 13-14 Oct |
| Conceptual Exam One Due | 20 Oct |
| Practical Exam One Due | 27 Oct |
| Conceptual Exam Two Due | 17 Nov |
| Practical Exam Two Due | 24 Nov |
| Thanksgiving Break | 26-30 Nov |
| Last Class | 10 Dec |
| Takehome Final Exam Due | 19 Dec |
Chemistry 331 is a Smith College course: the Honor Code applies. Any work that you submit for a grade must be your own work unless specifically indicated otherwise by the instructor. The individual quizzes, the two examinations, and the final examinations are work that you are expected to do on your own. Preparation of the daily problems may be the work of a group. You are STRONGLY encouraged to do problems with others.
<ψ|a+a-|ψ>
ψ(x,t) =
Σcnψn(x) e-iEt/hbar
[x, px] = i hbar
[x, py] = 0
p = - i hbar δ/δx
<x> = ∫ ψ* x ψ dx
H ψ = E ψ
ψ = A ei k x + B e-i k x