Physics
130B Fall 2011
Course Information
The only constant is change. You must check the class web site before each
class for changes: http://physics.ucsd.edu,
choose “Current Students”, “Academics”, “Course Web Pages”, or http://physics.ucsd.edu/students/courses/fall2011/physics130b.
Updated
9/19/2012 9:52:46 Section
722382
Announcements
Anonymous grade graphs posted.
Final exam solutions v6 posted. Extra credit if you find a mistake.
General Information
“Quantum Mechanics is a silly
theory, perhaps the silliest theory to come out of the 20th
century. The only reason it has any
following at all is that it is completely supported by experiment.” — Unknown
physicist
“If quantum mechanics hasn’t
profoundly shocked you, you haven’t understood it yet” — Neils Bohr
“Now in the further development of
science, we want more than just a formula.
First we have an observation, then we have numbers that we measure, then
we have a law which summarizes all the numbers.
But the real glory of science is that we can find a way of
thinking such that the law is evident.”
— Richard Feynman, The Feynman Lectures on Physics, p26-3.
My main goal in this class is to facilitate a physical, intuitive, conceptual understanding of quantum mechanics. In other words, my goal is to refute the first quote above, and illustrate the second, thus satisfying the third. This will make the mathematics much more meaningful.
Smart people ask questions. That’s how they got that way. Every question is a good question.
If you send me email about an administrative issue, do not assume I remember anything we talked about (there are lots of students). Please include a summary of any discussion in your email, so I’ll know to what you refer.
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Instructor |
Dr. Eric L. Michelsen |
Office hours: |
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Teaching Assistant |
Casey Conger |
Office hours: Th 4:00-5:30, Mayer Hall
Addition 4523 (all the way in the back corner near York) |
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Text |
Quantum Processes Systems & Information, Benjamin Schumacher, Michael Westmoreland. Cambridge University Press (April 26, 2010) ISBN-10: 052187534X ISBN-13: 978-0521875349 |
I have requested a copy be on reserve in the library. You can also read it free on the web from the library web site (look it up in Roger). |
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Course coordinator |
Patti Hey |
2571 Mayer Hall Addition, 822-1468, plhey@physics.ucsd.edu |
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Lecture times |
MWF
11:00am - 11:50am WLH 2111 |
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Discussion |
Wednesday 4:00-4:50, Pepper Canyon Hall 121 |
Attendance optional. See below. |
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Midterms |
TBD |
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Final Exam |
12/06/2011 Tu |
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Physics Department Tutorial Center |
Sunday-Thursday from 3-8 p.m. |
2702 Mayer Hall Addition |
Check the Schedule of Classes for updates:
https://www-act.ucsd.edu/cgi-bin/tritonlink.pl/7/students/academic/classes/class_schedule.pl
Thank you to Dr. Abarbanel and Dr. Sham for their help in preparing this class.
Cool Websites
My Funky Physics tutorials: http://physics.ucsd.edu/~emichels/ . Phasors are described there in Funky Electromagnetic Concepts. Let me know if you want to be on my email list to get new articles in the Funky Series as they are drafted.
Quantum harmonic oscillator video:
http://www.youtube.com/watch?v=VWxMPjDo3Ak&feature=related
Course Description
Physics 130B is the second quarter of a 3-quarter sequence. The course is aimed at students majoring in science and engineering, especially physics. It is a continuation of Physics 130A. We will follow the book as much as we can, but likely in a different order, and with some additions.
We want you to succeed. As part of that, we expect you to read ahead of the class, and start the homework even as it is being discussed in class. I don't cover every topic in class; some I leave to the book. I encourage questions in class, but if you want more individual questions answered, I also recommend going to the office hours, discussion/problem sessions, and the Physics Tutorial Center.
Prerequisites
Physics 130A, partial differential equations. Integral and differential calculus of multivariate functions is required. A basic knowledge of partial differential equations is essential. You must understand complex functions, exponentials, derivatives, and integrals. In particular, you must understand the polar forms of complex multiplication and division. Phasors are crucial. It is very helpful to understand basic statistics, and linear algebra (matrices).
Funky Quantum Concepts (on the web page given above) has a review of the complex number theory you’ll need.
Discussion and Problem Sessions
There is a weekly discussion session, hosted by the TA. The topics are driven by student questions during the session. This is a chance for you to get answers to your questions. After working on the homework, please come with good questions. You should ask, “I tried doing the problem this way, and ran into a roadblock. Can you help me through it?” Or, “What concept do I use to get started on this problem?” (You should not ask, “How do I do this problem?”)
Discussion is over when the questions end, and the TA is satisfied.
Homework
The purpose of homework is to help
learning.
To understand the material, you must practice solving problems.
Problems will be assigned roughly weekly. Homework is part of your grade.
Just like in the real world, clarity and ease of reading count. Please staple pages together, and put your full name and Student ID on every page. No ragged spiral edges, please.
The first step in solving a problem is often the most difficult, so it is very important for you to start work on your own. After you’ve made an effort on each problem, I encourage you to work in groups, but in the end, the homework you turn in must be your own work, and you will be expected to be able to answer questions and reproduce any part of it.
Learning physics is about understanding why a solution works,
rather than just getting the correct results.
Blindly plugging into formulas is useless.
Late homework should be dropped at the TA’s office (slip under door if needed), as soon as you can. Late homework may be marked down.
Midterms
- There are no make-up exams. If you anticipate missing an exam due to unavoidable circumstances, you must discuss this with the instructor in the first week. There is no guarantee that you can be accommodated, and you will likely have to drop or withdraw from the class.
- Please do not ask to take any exam early or late; to be fair to everyone, the answer is always “No.”
- Exams may ask about any concept discussed in class or in HW. They may be different than HW questions, though some may be similar.
- All exams are cumulative, and may include anything covered so far.
- You may wish to bring some blank scratch paper to the exam.
Final Exam
Your student I.D. is required to take the final exam.
The final will be like a big midterm. You may wish to bring some blank scratch paper.
Course Grade
HW, midterm, final, class participation all count. Extra credit for finding a mistake in my online Funky notes.
Plusses and minuses at instructor discretion. Actual grades may be higher if warranted by overall class performance, but don’t count on it.
Academic Integrity
Every honest student benefits from maintaining high academic integrity. Please read “UCSD Policy on Integrity of Scholarship” in the UCSD General Catalog, http://www.ucsd.edu/catalog/front/AcadRegu.html. These rules will be rigorously enforced. Any confirmed case of cheating will result in an “F” grade in this course, and referral to the dean for disciplinary action. Cheating includes submitting another person’s work as your own; copying from another student on homework, or exams; knowingly allowing another student to copy from you; use of unauthorized materials during a quiz or exam; or any attempt to obtain a higher grade by means other than honest effort. Cheating also includes attempts to manipulate grades unfairly; and intentionally misusing code numbers.
Course Notes
Book Corrections and Clarifications
Will be updated as needed.
Chapter 1: The book’s discussion of “phases” and “amplitudes” (p16) appears to sometimes confuse “phase” and “amplitude”. “Complex amplitude” includes magnitude and phase. “Instantaneous amplitude” is always real, and can be computed from magnitude, phase, and time, but the reverse is not true. “Phase” is a real angle giving the starting angle of a sinusoid.
I disagree with P17’s characterization of the use of complex numbers in QM. They are used similarly to those in mechanics and EM. One can do QM without them, but it is messy. QM complex numbers are related to phasors and transfer functions, and greatly simplify the math.
Chapter 2: P40, below Ex. 2.26: “ω2 – ω1” should be “ω1 – ω0”.
P40: Operators, in general, need not be linear, though in QM all but one operator is linear. We will not use it in this course, but the time-reversal operator is not linear; it is anti-linear.
Chapter 3: P73m: We need not assume the relation for spin operators in arbitrary directions is the same as the classical form: this is guaranteed by the behavior of operators.
Chapter 4: Wave-function collapse is an advanced topic that is difficult to understand, and related to “decoherence.” The discussion of wave-function collapse can be confusing (p85-7). I believe that in most models of QM, machines cannot make “observations,” and cannot collapse a wave function. Only an observer can collapse his own wave function, though decoherence can reduce measurements to classical behavior. The collapse of the wave-function is relative to the observer. More on this in class.
The discussion of quantum cryptography (p88-91) leaves out an important part of Eve’s behavior: she is acting as a “(wo)man in the middle”. She attempts to intercept Alice’s message, and retransmit it to Bob, without either of them knowing.
Chapter 6: p117, after eq. 6.1: they use the term “correlation” (as is common in quantum mechanics), though it is more strict to use “dependence.” Eq. 6.2 is the definition of statistical independence, not correlation. Note that Ex. 6.28 p129 correctly uses the term “independent” when referring to eq. 6.2.
Chapter 10: p205t and p207t: I believe the kets |x> are, indeed, vectors in a Hilbert space, but not the space of unit-normalized wave-functions. This is related to δ-function normalization, which is tedious, but I think mathematically valid.
Problem 10.1 p222t: |ψ> is unique only up to a complex phase.
Chapter 13: p268, 2nd line: ‘... “ladder” of Sx ...’ should say ‘... “ladder” of Sz ...’.
p273m: The book sometimes correctly distinguishes the number 0 from the zero-vector, which they write as bold “0” (I write as “0v”). However, just above eq. 13.27 should read “... a|0> = 0v.” This is the null ket, aka “zero-vector”.
Chapter 17: Eq. 17.6 is missing the summations and |k> kets. It should read:
Week 0/1: 9/23
See Funky Quantum Concepts (on the web page given above) for a description of the Greek alphabet, and a brief review of complex numbers.
Phasors are a critical concept in QM (and indeed, all of physics). See Funky Electromagnetic Concepts for a description of phasors. We will use their concepts extensively. The wave-function can be thought of as a phasor-valued function of space.
HW1_corrected.pdf due Wednesday, 9/28/2011. It is entirely review, and you should be able to do all of it already. Future homework will be more challenging.
Deriving the Schrödinger equation from the axioms.
Week 2: 10/3
HW2_clarified_hints.pdf due Friday in class.
Week 3: 10/10
HW3_v5.pdf due 10/14 in class.
Week 4: 10/17
HW4_v3.pdf Due 10/21 in class.
Week 5: 10/24
HW5_v4.pdf HW5 due date pushed back to Monday 10/31 (scary?), in deference to Statistical Mechanics. However, HW5 will be on midterm. I’ll post solutions after class on Monday.
Week 6: 10/31
Bring a blue book for the midterm on Wednesday 11/2/2011. All material in class, and through and including HW5. No HW week 6. 130B_midterm_solutions_v5.pdf
“Best 3 out of 4” midterm scores:
7 (–2σ) 16 19 20 21 21 24 (–1σ) 39 39 39 40 40 40 41 41 43 44 45 47 47 avg = 51, σ = 20
52 52 53 55 56 59 63 64 65 65 65 67 69 69 71 (+1σ) 73 73 77 84 88 (+2σ) 93
Week 7: 11/7
HW6 beginnings, due Monday 11/14/2011: HW6_v3.pdf
Friday 11/11 Veteran’s Day
Week 8: 11/14
HW7_v2.pdf complete, due Monday 11/21.
Week 9: 11/21
HW8_v4.pdf, due
Wednesday 11/30/2011.
Th-Fr Thanksgiving.
Week 10: 11/28
HW9_v2.pdf final. Not collected, but will be on Final Exam. Note correction to chapter 17 above.
Final Examination:
Bring a blue book (or two) for the final exam. Review session info posted above.
avg = 76, σ = 13
39 43 (–2σ) 54 56 61 (–1σ) 65 66 66 67 67 68 71 71 73 73 74
77 78 79 80 80 81 81 81 82 83 83 84 84 84 85 85 85 86 87 87 (1σ) 90 90 90 94 95
Final grades weighted: Hw 30%, Midterm 30%, Final 30%, Participation 10%.