Physics 356F
Introduction to Quantum Physics.

(last updated 7 Sep 2014)


Lecturer:
Aephraim M. Steinberg
(rm 1103, tel 978-0713, my last name at physics.utoronto.ca)

Office hours: (tentatively Thursdays 3-4;
feel free to let me know in advance if you believe a significant segment of the class would have a conflict with this time)
[one-on-one meetings also always possible by appointment]


Teaching Assistants:

Derek Inman
Zachary Vernon


Times and Venues
Lectures: Mondays & Wednesdays, 12:10 in MP102
Discussion section times : Tuesdays (TUT 0101 & 0102) or Thursdays (for TUT 0201 & 0202), 12:10
Discussion section venues: last names beginning with letters A-K in SS1084; last names beginning with letters L-Z in SS1086

FIRST LECTURE ON SEPTEMBER 8th;
FIRST TUTORIALS TO BE HELD ON SEPTEMBER 9th AND 11th (depending on your section assignment; see above)

Course Web Page

This course will use the Piazza website.
Please sign up at this link immediately.
Assignments, readings, and announcements will be posted on the Piazza website.
You are also strongly encouraged to use Piazza to post questions about the course material, where both the instructors and your fellow students will be able to engage in discussions about it.
(Blackboard will only be used for posting grades.)

Overview | Grading | Syllabus | Announcements | Readings | Postings | Tutorials | Problem Sets |


Overview

Quantum physics is one of the major scientific and intellectual developments of the 20th century. Not only has it revolutionized Man's understanding of the structure of matter, but it underpins a broad cross-section of modern technology, from the transistors in your computer to the laser in your CD player. More than that, however, it has led to a radical change in the basic structure of how we understand the world. This change is not limited to atoms, or even to the microscopic world in general. It applies whether we are discussing electric forces, angular momentum, light, matter, or the nuclear forces.

In this course, we will study the structure and postulates of quantum mechanics and will then develop the basic mathematical and conceptual tools to deal with important topics such as angular momentum, the Hydrogen atom, the harmonic oscillator, entanglement, indistinguishable particles, and spin. In parallel, you will be challenged to develop your intuition about the quantum world, with discussions based largely on two-level systems such as the Stern-Gerlach experiment, photon polarization, and two-slit (or Mach-Zehnder) interferometers.

The required text is Townsend's A Modern Approach to Quantum Mechanics.

For further reading, I strongly recommend Richard P. Feynman's wonderful QED: the strange theory of light and matter, as well as the following alternate textbooks:
Shankar's Principles of Quantum Mechanics
Feynman's Lectures on Physics vol. III

Grading

Fraction of Grade
Problem Sets 20%
Mid Term 30%
Final Exam 50%

There will be 4 or 5 problem sets over the course of the semester. The problem sets are to be handed in at the tutorial sessions.
Only selected problems will be marked; the purpose of the assignments is not primarily evaluation of your performance, but rather to give you the opportunity to work through the material, develop your understanding, and also prepare for the exams. Solution sets will be posted after the problem sets are handed in, and obviously this means that no late assignments can be accepted.

Syllabus

Quantum mechanics is a challenging subject because it forces us to come to terms with completely new ideas of how reality should be described and what can be predicted, and not merely because it involves solving a particular second-order partial differential equation. Quantum mechanics is not just a theory of electrons in atoms, or even of microscopic particles in general, but as some wag (I've forgotten who) put it, "the Operating System under which all other physics theories run."

While this course will endeavour to give you the tools to solve many of the important classes of problems you are likely to encounted as you continue studying physics, it will also stress the fundamental features that make quantum physics truly different from classical physics, and attempt to develop your intuitions about quantum phenomena. We will approach quantum mechanics in an axiomatic fashion, and do our best to understand what leads us to believe these axioms, and what their significance is. I will also introduce, briefly, some of the modern "applications" of quantum physics such as quantum computation and quantum teleportation, although along the way we plan to resolve some more prosaic questions such as why the spectrum of Hydrogen is what it is and why the periodic table looks the way it does.

Because of the thorny conceptual issues involved in quantum mechanics, while I will use most lectures to cover to cover some standard, "technical," "textbook" material, I will devote a number of the lectures to more "complementary" issues.

Class participation is encouraged during all lectures, and particularly during the concept-based "complements," when students should be prepared to discuss questions in small groups and then defend their conclusions (or raise new questions). You will find that active participation in discussions is essential for developing a real understanding of the material, and this will be reflected both on the exams and in the writing assignments.

The lectures will break down into 6 units, of approximately two weeks apiece. The following tentative syllabus indicates the material I would ideally like to cover by the end of term, and likely topics for the "complements." Naturally, some topics may need to be shortened or omitted entirely in order to finish in 12 weeks, but we begin in a spirit of optimism!

(The most relevant readings are listed along with the subject headings below, although we will not be following the book religiously, and some topics are not treated there at all.)

UNIT "Technical" lectures "Conceptual" complements
1 Photon polarisation and electron spin;
the phenomena of quantum measurement (ch's 1-2)
Single-photon and single-electron interference (QED; see also ch. 8 of Townsend);
quantum cryptography
2 The structure and postulates of QM;
matrix mechanics and Dirac notation (ch 2; Shankar ch's 4 & 1)
Interaction-free measurement;
the quantum eraser
3 Commutation, conservation, and uncertainty;
time evolution (ch's 3-4)
Quantum jumps and the Quantum Zeno Effect
4 Wave mechanics and the harmonic oscillator (ch's 6-7) Measurements and correlations;
the Einstein-Podolsky Rosen "paradox" and Bell's inequalities (ch 5)
5 Separation of variables, multi-dimensional problems, and angular momentum (ch's 3 and 9) Quantum teleportation;
quantum computation
6 The Hydrogen atom;
indistinguishable particles (ch's 9,10, and 12)
If time permits, some real-world examples


Announcements and Recommended Readings


The sections in Townsend most relevant to each section of the course are listed along with the syllabus given above. You will be expected to keep up with the reading. Sometimes, additional sources may be suggested, especially for the complements.

For interference and probability amplitudes, I recommend the following references:
Feynman's QED
Feynman's Lectures on Physics, vol. III, ch's 1-3.

For two-state systems, ch's 5 and 6 of Feynman vol. III may prove useful.

For the postulates of quantum mechanics, Shankar's Principles of Quantum Mechanics is a very clear reference.

For philosophical and interpretational aspects, including great detail on the debates between Bohr and Einstein, I suggest
Wheeler & Zurek, Quantum Theory and Measurement and
Bell, Speakable and Unspeakable in Quantum Mechanics.

The following articles may be accessible introductions to some of the more modern experiments and issues in quantum mechanics, related to the complements:
Horgan, "Quantum Philosophy," Sci. Am. 267 (1), 94 (7/92).
Bennett et al., "Quantum Cryptography," Sci. Am. 10/92
Chiao et al., "Faster than light?", Sci. Am. 8/93
Greenberger et al., "Multiparticle Interferometry," Physics Today 46 (8), 22 (8/93)
Kwiat et al., "Quantum Seeing in The Dark," Sci. Am. 275 (5), 52 (11/96).
Scully et al., "Quantum optical tests of complementarity," Nature 351, 111 (1991)
Zurek, "Decoherence and the transition from quantum to classical," Physics Today 44, 36 (1991)
Collins, "Quantum Cryptography," Physics Today 45, 21 (1992).


A very nice page on "Visual Quantum Mechanics," with useful material for review, can be found here.

Posted Lectures & Readings


For the first two weeks, you should finish reading the first two chapters of Townsend, as indicated on the syllabus. It may be interesting to start with section 2.7, on photon polarisation, since this is the approach we are taking in class (mathematically equivalent to the Stern-Gerlach problem treated in chapter 1).

For those of you not sufficiently comfortable with polarized light, I strongly recommend first reading David Harrison's short introduction, and/or the Wikipedia page on polarizers.

For the material on two-slit interference, I know of no better reference than the Feynman book on "QED: The Strange Theory of Light and Matter."
The Wikipedia page is all right, and links to discussions of "complementarity" and the "quantum eraser," topics which we will continue discussing along with the "Feynman rules." Its discussion of the "path-integral formulation" is the mathematically more general description of what I've been calling Feynman's rules.

Problem Sets

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