Instructor Insights

Course Overview

This page focuses on the course 8.06 Quantum Physics III as it was taught by Professor Aram Harrow in Spring 2016.

This course is a continuation of 8.05 Quantum Physics II. Topics include units, time-independent approximation methods, the structure of one- and two-electron atoms, charged particles in a magnetic field and time-dependent perturbation theory. Students research and write a paper on a topic related to the content of 8.05 and 8.06.

Course Outcomes

Course Goals for Students

Interpret and analyze a wide range of quantum mechanical systems using both exact analytic techniques and various approximation methods.
Gain an introduction to important model systems studied in contemporary physics, including white dwarf stars, two dimensional electron systems, the fine structure of Hydrogen, lasers, and particle scattering.

Curriculum Information

Prerequisites

8.05 Quantum Physics II

Requirements Satisfied

CI-M

Offered

Every spring semester

Instructor Insights

"I’ve to come to realize there are three things I need to teach related to each topic: the physical principle, the technique related to the principle, and an application of the technique."

— Aram Harrow

In the following pages, Aram Harrow describes various aspects of how he teaches 8.06 Quantum Physics III.

Student Information

Enrollment

41 students

Breakdown by Year

Mostly juniors

Breakdown by Major

Mostly physics and math majors

Assessment

Grade Breakdown

The students’ grades were based on the following activities:

25% Problem Sets
15% Midterm
25% Term Paper
35% Final Exam

Instructor Insights on Assessment

Please see Prof. Aram Harrow’s instructor insights about providing students with feedback on their writing.

How Student Time Was Spent

During an average week, students were expected to spend 12 hours on the course, roughly divided as follows:

Lecture

Met 2 times per week for 1.5 hours per session; 27 sessions total.

Recitation

Met 2 times per week for 1 hour per session; 25 sessions total.

Out of Class

Problem sets
Term paper
Exam preparation

In this section, Prof. Aram Harrow describes the term paper assignment in 8.06 Quantum Physics III and shares its two-fold purpose.

Students in 8.06 Quantum Physics III are expected to research and write a short paper on a topic related to the content of 8.05 Quantum Physics II or 8.06 Quantum Physics III. The paper can explain a physical effect or further explicate ideas or problems covered in the courses. It can be based on students’ own calculations and/or library research. The paper should be written in the style and format of a brief journal article and should be aimed at an audience of 8.06 students.

"By the time they take this course, students have learned enough to be able to independently research and write about a quantum physics topic. One of the goals of the term paper assignment is to demonstrate for students that this is possible."

— Aram Harrow

8.06 Quantum Physics III is the final course in the undergraduate physics sequence. By the time they take this course, students have learned enough to be able to independently research and write about a quantum physics topic. One of the goals of the term paper assignment is to demonstrate for students that this is possible.

Another goal is for students to experience writing a polished essay. It’s a process. It starts with the students choosing a topic. We give them suggestions, but also encourage them to come up with their own topics. The students then develop proposals. Students write multiple drafts of their term papers and receive feedback from peers, professors, and teaching assistants exclusively hired to support students in their writing. There’s a lot of revision and feedback that go into the papers. At the end of the course, students receive a bound copy of all the final papers.

In this section, Prof. Aram Harrow shares his approach for providing students with productive feedback about their writing.

Providing students with productive feedback about their writing can be challenging because there so many different aspects of a paper an instructor might focus on. To address this challenge, I try to tailor my feedback to match the writer’s stage of paper development. I don’t correct grammar on a rough draft, for instance. I save that kind of feedback for later iterations.

"I provide feedback that helps (students) plan in such a way that, even if they were to complete only the first part of their proposals, their papers would be successful. This allows the students to be both realistic and ambitious at the same time."

— Aram Harrow

In addition to providing students with feedback on the mechanics of their writing, I also provide them with feedback on their strategy for planning and executing a paper. I used to get really excited when a student would tell me they planned to do something ambitious in their paper. Now, I realize that they may not see how much work they’ve bitten off. We have a page limit for the term paper in 8.06 Quantum Mechanics III and there’s a time limit for how long students can work on their papers. When students come to me with ambitious proposals, I think carefully about the scope of their intentions. I ask students to identify their goals and sub-goals and to think about how they will accomplish the work they’ve set out to do given the constraints of the assignment.

But, of course, I don’t want to discourage them, so I also ask, “Which part of this proposal would you work on first? Which part would you focus on next?” I provide feedback that helps them plan in such a way that, even if they were to complete only the first part of their proposals, their papers would be successful. This allows the students to be both realistic and ambitious at the same time. This strategy for providing feedback has been useful because it recognizes that students’ energy comes in waves during the semester. There’s a time (usually toward the beginning of the semester) when students are energetic and feel they can do anything; and then there’s another period when they’re scrambling. Providing feedback that works with, instead of against, this ebb and flow of energy has been productive.

In this section, Prof. Aram Harrow shares how he determines what materials to cover in this fast-paced lecture course.

The 8.06 Quantum Physics III curriculum is extremely fast-paced. We cover a wide range of topics and I have to select what material, related to each topic, to include in each lecture. It can be daunting.

"I select materials for lectures based on whether they’ll help me teach a physical principle, a technique or an application."

— Aram Harrow

I’ve to come to realize there are three things I need to teach related to each topic: the physical principle, the technique related to the principle, and an application of the technique. If I don’t teach the application, the technique can be very dry and abstract. Without the application, it’s hard for students to remember the technique, and difficult for them to get a sense for how it should work. If I don’t teach the physical principle, students won’t understand the larger framework shaping the technique and the application. I need all three elements in each lecture. Accordingly, I select materials for lectures based on whether they’ll help me teach a physical principle, a technique or an application. If a particular material doesn’t help me teach one of these elements, I have a hard time justifying its inclusion in the lecture and usually leave it out.

In planning for lectures, I also consider how to get from one element to the next. For example, I think about the minimum amount of information I need to share with students to help them move from technique to application. If information is extraneous to this purpose, I look at it skeptically. I think about lecture material in terms of what is essential, and what is bonus material.

In this section, Prof. Aram Harrow shares his approach for helping students move forward when they become stuck during problem solving.

"Usually students get stuck on a problem because they possess a brittle understanding of the technique involved in solving it."

— Aram Harrow

Usually students get stuck on a problem because they possess a brittle understanding of the technique involved in solving it. They know how to apply the technique in one context, but they don’t understand the larger framework in which it’s embedded. When I can get students to explain why they’re solving a problem in a particular way, I expose misunderstandings they have about the bigger concepts involved in the problem, and this helps me support them strategically.

Assuming the problem set isn’t due the next day and I have ample time to support a student stuck on a problem, I take a Socratic approach to help the student explain how he or she is thinking about the problem. I ask the student why he or she is approaching the problem in a particular way, what he or she knows about different approaches for solving the problem, and why the student thinks one approach might be more or less productive than another. This dialogue seems to helps students move forward with solving the problem.

I also look at students’ calculations, and point out simplifications they might not have seen. I think sometimes students learn a certain way of doing something, and they might do it 100 times and never realize that they could have been doing it differently the whole time. They could get the answer either way, but if they do it the simpler way, their solutions might be less prone to errors. Although pointing out simplifications might not help students get “un-stuck,” when solving problems, it is an important part of supporting their overall problem-solving endeavors.

In this section, Prof. Aram Harrow describes how teaching recitations in 8.05 Quantum Physics II helps him anticipate material students might find challenging during 8.06 Quantum Physics III lectures.

"Getting to know students during the 8.05 recitations helps me identify concepts they may find challenging during 8.06 lectures."

— Aram Harrow

8.06 Quantum III is a continuation of 8.05 Quantum Physics II. I teach recitation sessions in 8.05, and then I teach many of the same students during lectures in 8.06. Getting to know students during the 8.05 recitations helps me identify concepts they may find challenging during 8.06 lectures. This is particularly helpful as I tend not to get extensive feedback from students during lectures about what they misunderstand.

I also have experience teaching recitations for 8.06 Quantum Physics III. Within the physics department, it’s not uncommon to teach recitations before lecturing in a course. It’s great when this can happen because recitations are where students work through the course material and you, as the instructor, get to understand how they’re thinking about the material and where their misconceptions lie.

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Quantum Physics III

Instructor Insights

Course Overview

Course Outcomes

Course Goals for Students

Curriculum Information

Prerequisites

Requirements Satisfied

Offered

Instructor Insights

Student Information

Enrollment

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Breakdown by Major

Assessment

Grade Breakdown

Instructor Insights on Assessment

How Student Time Was Spent

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Out of Class

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