PHY 307 - Fall 2011
Stony Brook University
Department of Physics and Astronomy
College of Arts and Sciences
Course Instructor:
Alfred Scharff Goldhaber
goldhab 
max2.physics.sunysb.edu, 631 632 7975, fax 631 632 7954. Office Math 6-113.
Recitatiosn: Sec. 1 W 1145 a.m.-1240 p.m., Physics P-119
Sec. 2 W 1250 p.m.-145 p.m., Physics P-119
Course credits: Four credits corresponding to four contact hours
Office Hours: To be determined, plus by appointment at class, on the phone, or on email
INTENDED AUDIENCE:
As described below, this course is designed to be fully accessible to students who have completed one year of introductory physics and the associated introductory calculus [If Modern Physics, PHY 251, is taken at the same time, the two courses should reinforce each other; the same applies for PHY 300, PHY 301, and PHY 405]. For such students the intent is that they should feel as if they were "gliding into quantum mechanics." As with hang gliding, first it is necessary to climb to a high place. In this case the "high place" is the properties of electromagnetic waves, well worth mastering in their own right. Students who already have more background, including Waves and Optics (PHY 300) and Electromagnetic Theory I, II (PHY 301, 302) as well as Quantum Physics (our standard introductory course, PHY 308) and Advanced Quantum Physics (PHY 405) can benefit as well, because important and subtle concepts they have seen already are approached from a different perspective, reinforcing the learning.
COURSE DESCRIPTION:
Physical and mathematical foundations of quantum mechanics. Maxwell waves and their properties: Intensity, energy density, momentum density. Complementary descriptions of wave superpositions in position and in "wave number." Planck-Einstein relation between energy and frequency for light quanta. De Broglie relation between momentum and wavelength. Number density and probability density of photons. One-photon quantum mechanics, with Maxwell field as the wave function. Diffraction phenomena. Uncertainty relation between wave number and position, hence between momentum and position. Three lecture hours and one recitation hour per week.
Course pre- and co-requisites
Pre-requisites -- Introductory classical mechanics and electromagnetism. Introductory differential and integral calculus. Advisory co-requisite -- Multivariable calculus. [Because the Maxwell equations involve three space dimensions, and time, for the vector electric and magnetic fields, they give a wonderful laboratory for working with multivariable calculus.] Having that course beforehand or concurrently would give extra and possibly complementary perspective on these properties, but all that is needed will be worked out fully in PHY 307. Course numbers: PHY 122, or 127, or 132, or 142, MAT 132 or 142 or 127 or 171 or AMS 161. Advisory co-requisite: MAT 203, MAT 205, or equivalent. Students who took and passed Physical and Mathematical Foundations of Quantum Mechanics under the previous course numbers PHY 390 and PHY 274 are ineligible to take PHY 307. PHY 307, while not required for the major like other courses including PHY 251 and PHY 308, is intended to provide a "keystone" which stabilizes the entire arc of undergraduate quantum studies.
MOTIVATION:
For more than eight decades the teaching of quantum mechanics has followed two main tracks. The first approach is at least partly historical. There is some logic to that, because if people originally found things in a certain sequence then it is at least possible for students to learn in that sequence. This is the style of "modern physics" courses, which give a broad survey of phenomena especially in microscopic physics, including many of the steps in the somewhat contorted path that led to modern quantum mechanics.
The other method is axiomatic, exemplified by Dirac's great book on the subject, a pattern followed by many more recent texts. In my opinion there is a missing piece in this traditional two-tiered approach. The intellectual jump from the broad survey to the axiomatic treatment is not easily articulated, and can be disconcerting for students as they try to negotiate the transition. The approach of the present course could be called "quasi-historical," meaning to build on a history that might have been if Einstein in 1905 had shown even greater audacity than he did in his "photoelectric effect" paper. The aim is to provide a path that is as short and direct as possible from 1905 to 1925-6, when Heisenberg and Schrödinger introduced the theory we still have today.
If short, this climb can be quite challenging, and requires an intense study of Maxwell's electromagnetic waves and their properties to provide the foundation for the ascent. The take-home message, as in Einstein's special theory of relativity, is that when one tries to fit together Maxwell's theory with other knowledge, in case of doubt one should defer to Maxwell. This may seem natural when one recognizes that Maxwell's is the first fundamental field theory in physics, still unaltered at the classical level nearly 150 years after its formulation. Thus the new course complements not only the existing one on modern physics but also other departmental offerings on aspects of electromagnetism and light. The path, as indicated in the syllabus below, goes through Maxwell electrodynamics to one-photon quantum mechanics, and uses that as a base to develop one-electron quantum mechanics. I call this way "stronger, deeper, better" [Stronger: there is an organic connection to electrodynamics, which leads through Einstein's light quanta to photon quantum mechanics. Deeper: The two essential notions of quantized energy and photon intensity give a base for everything else. Better: These two notions allow deduction in a natural and straightforward way of most if not all the remarkable and puzzling features of quantum physics, replacing the abrupt transition from a modern physics course to a formal course.] I believe this approach could help overcome what seems to me a deficiency in current physics training, that students are exposed to classical mechanics and classical electrodynamics twice during their undergraduate years, but a systematic approach to quantum physics just comes along at the end. My idea is that this should be a first-term sophomore course, simultaneous with and complementing the Modern Physics course, allowing students to enter PHY 308, Quantum Physics, in the spring of sophomore year. This would be a one-year speed-up compared to the current pattern here, and would put our program on the same pace (with respect to quantum physics) as many other colleges. Colleagues at a number of other institutions have introduced quantum mechanics through light rather than through massive particles like electrons, but I'm unaware of any textbook which does this. As mentioned above, another way to view the goal of this course is "gliding into quantum mechanics." The climb to begin the glide is through understanding the Maxwell equations and their free solutions, the first-discovered fundamental waves in physics. After learning about electromagnetic waves and wave packets, we can recognize these solutions as quantum-mechanical waves describing the behavior of photons, or particles of light.
COURSE OBJECTIVES:
Complements PHY 251 Modern Physics and prepares a foundation for PHY 308 Quantum Physics, by first arriving at one photon-quantum mechanics through the principles indicated (thought not fully worked out) in Einstein's 1905 paper on the photo-electric effect, and then deriving the Schrödinger equation. Also useful for students who already have taken PHY 308, and PHY 405, because it gives further insight into many of the issues introduced there.
COURSE REQUIREMENTS:
Attendance and Make Up Policy
One-half point homework-problem credit per class for attendance after the add-drop period, and one-third point for recitation attendance. Half-credit for each late arrival. Late homework may be graded down, depending on circumstances. Both for homework and for attendance excused lateness or absence will not count against the student.
Required books
Two required textbooks (#1 and #2), and one reference book (#3) from the Schaum Outline Series:
Exams
None.
Paper and Presentation
Each student is asked to prepare a 5-page paper and make a 4-minute class presentation about the topic of the paper. If two people work together on a paper and presentation, each will get the same grade, but then the paper and presentation should be twice as long, for three people three times as long, etc. The topic of the paper and presentation can be anything that appears in the historical background for quantum mechanics, including experimental discoveries such as what we now know as atomic spectra (many important examples that different papers could discuss), Wien's approximate formula for the black-body radiation which laid the groundwork for Planck, conceptual proposals such as the molecular hypothesis (in its ancient form with Demokritos and Lucretius, or its later form with Dalton). A list of possible topics will be distributed early in the course. Students may choose a topic from the list (first-come first served), or propose a different topic for approval.
Grading
Ten homework sets during the term, with a possible 5 points for each set (one per problem). One-half point for attendance at each lecture, and one-third point for attendance at each recitation, after the end of the add-drop period (i.e., beginning Tuesday, 13 September). This adds up to a possible 16 points for the semester. Lateness cuts the grade for a particular attendance in half. Excused absence or lateness will not be penalized. Up to 20 points for the paper and presentation. One point extra credit for each homework set on which two to four people have cooperated in discussing the homework, before writing up the solutions separately. Up to 14 points for valuable comments or questions in class, or on Blackboard. A new possibility: There will be regular opportunities to write from memory short descriptions of the content of each lecture, and post the writing confidentially on Blackboard. The reason is that recent research suggests students who do such an exercise retain the material much better than students who use other strategies to solidify the information. These writings will be good for extra credit only, so there will be no penalty for those who do not wish to do the writing.
Letter grades: >95=A, >90 =A-, >85=B+, >80=B, >75=B-, >70=C+, >65=C, >60=C-. Actual letter grades will not be lower than implied by these guidelines, but might be higher.
MEETING SCHEDULE
[NOTE: FROM PREVIOUS EXPERIENCE, SOME OF THESE ITEMS MAY TAKE MORE THAN ONE LECTURE -- THERE IS A RESERVE OF FOUR LECTURE PERIODS TO ACCOMMODATE THIS]
No exams. Lecture plan:
Recitations: The first meetings of the recitations will take place the first week, and will be for getting acquainted and exploring student hopes for the course. After that, in a week with homework due the following day, questions and discussions about the homework will be the principal business, though other questions about lecture material also will be welcome.
CLASS PROTOCOL
Cell phone and electronic device statement: Everyone, including the instructor, is permitted to bring devices to class, but they must be in quiet mode. Under normal circumstances, incoming calls should not be answered during class. Students are free to make audio or video recordings of the class, and are permitted to post these recordings on the blackboard site. Our lecture classroom is equipped for video-recording, and the video-record will be made available through Blackboard.
CLASS RESOURCES
Library resources: Some texts will be put on reserve in the Math-Physics library.
Blackboard will be used extensively, and students are strongly encouraged to post comments or questions relating to the class, anonymously if they wish. Of course, to get credit for an apt comment or question, one must post eponymously!
DISABILITY SUPPORT SERVICES (DSS) STATEMENT
If you have a physical, psychological, medical or learning disability that may impact your course work, please contact Disability Support Services, ECC (Educational Communications Center) Building, room128, (631) 632-6748. They will determine with you what accommodations, if any, are necessary and appropriate. All information and documentation is confidential.
Students who require assistance during emergency evacuation are encouraged to discuss their needs with their professors and Disability Support Services. For procedures and information go to the following website: http://www.stonybrook.edu/ehs/fire/disabilities
ACADEMIC INTEGRITY STATEMENT
Each student must pursue his or her academic goals honestly and be personally accountable for all submitted work. Representing another person's work as your own is always wrong. Faculty are required to report any suspected instances of academic dishonesty to the Academic Judiciary. For more comprehensive information on academic integrity, including categories of academic dishonesty, please refer to the academic judiciary website at http://www.stonybrook.edu/uaa/academicjudiciary/
For this course there are some extra aspects associated with two complementary approaches, cooperation and independence. If you cooperate in discussing the homework, you should indicate with whom you worked, but you should be independent in writing up the solutions. That means it is quite possible that two students who discussed a particular problem could get different grades for their solutions. On the papers and presentations it is crucial to indicate all sources for significant statements you make. If you are quoting somebody, you should put the statement in quotation marks and indicate where you got it. If your source is a web presentation, you should indicate where it is (i.e., the URL), and the author if any is given, but you also should check it, as there are many incorrect statements in web presentations.
CRITICAL INCIDENT MANAGEMENT
Stony Brook University expects students to respect the rights, privileges, and property of other people. Faculty are required to report to the Office of Judicial Affairs any disruptive behavior that interrupts their ability to teach, compromises the safety of the learning environment, or inhibits students' ability to learn.