# General Exam Preparation

# Overview

The general exam consists of two parts: **written** and **oral**. See the department webpage for more details. The Written Exam addresses four topics:

- Electricity & Magnetism (E&M),
- Classical Mechanics (CM),
- Statistical Mechanics (SM),
- Quantum Mechanics (QM).

Students take each topic as a separate 75-minute exam, selecting one of two presented written questions; their performance is evaluated separately for each section. Students may also meet any one of the topic requirements through classwork (for E&M, 8.311; for CM, 8.309; for SM, 8.333; and for QM, 8.321). Written Exams are administered and results are available prior to the fall and spring semesters each year.

Sample exams, with solutions, are available to help MIT Physics doctoral students study for the Written Exam. Prior to 2015 our Qualifying Exams were given in 3 parts: Parts I and II comprised the Written Exam, and the Oral Exam was known as Part III. [Note that faculty and students who experienced the exams in this format may still refer to the current Written Exam as "Part II" and the Oral Exam as "Part III".] Sample exams labeled "Part II" with the 4 sections presented as a 5-hour exam continue to be valuable for Written Exam study, if reviewed as separate 75-minute topics. The fall 2015 is the first exam that was administered in the current format.

# MIT Physics GSC General Exam Report

In the spring of 2006, the MIT Physics GSC surveyed the Course 8 graduate student population on a series of topics relating to the Graduate General Exams. The results have been painstakingly compiled into a full report by the members of the PGSC. The PGSC has also prepared a report comparing MIT's general exams to those administered by other graduate physics programs in the US, and a collection of sample problems from exams at other universities. Many thanks to the MIT Physics GSC for this important service to the Course 8 graduate community!

# Written Exam Study Guide

The following study guide was generously contributed by Alexander Leder in 2015 and most recently reviewed by the faculty exam committee in 2019. It provides some useful tips and a list of topics for each of the four subject areas.

**[NEW!]** The following resources on Quantum Mechanics were generously contributed by Alex Yelland in 2023. Inside this ZIP file, there is both the PDF and TEX versions of his notes *(“Quantum_Mechanics_Notes”)*, the study guide *(“Quantum_Mechanics_Cheatsheet”)*, and the written exams solutions*(“Quantum_Mechanics_Written_Exams_Solutions”)*, along with the individual exam problems broken out into separate projects/PDFs. Please note that these resources were kindly provided by the student and they are not official. Please feel free to contact Alex (ayelland@mit.edu) or the PhysREFS (physREFS@mit.edu) if you have any questions or concerns.

**Sample Written Exams & Solutions**

**Below we have compiled exams and solution sets for as many back years as we can find. These are solutions generously provided by fellow students for past written exams; they are not official solutions. Please reach out to physREFS if you find any errors at physREFS@mit.edu**. **As you can see, not all exams have solution sets, and some of the posted solutions are messy or incomplete. If, in your preparation for the general exams, you work out a solution to a problem, please consider writing it up and sending us a copy. In addition to the warm, fuzzy sensation of knowing you helped out your fellow exam-takers, and the fame and prestige of having your insightful solution admired by future generations of Course 8 students, the really important thing is that every neatly typeset and correct solution to a complete written exam problem will be gratefully rewarded with a shiny physREFS water bottle. To qualify for the gift, the existing solution to the problem below must be either (1) missing, (2) handwritten, or (3) demonstrably incorrect (with the demonstrating to be done by you). Only submissions typeset in LaTeX will be accepted; you must send us both the PDF and LaTeX source versions of your solution. Send your submissions to physREFS@mit.edu.**

**2021 Fall: Exam | Student contributions: Classical Mech. 1 & 2 by Rikab Gambhir and Daniel Mark, Statistical Mech. 1 & 2 by Yunchao Zhang, EM 1 & 2 by Yunchao Zhang, QM 1 & 2 by Zhaoyi Li****2021 Spring: Exam | Student contributions: Classical Mech. 1 & 2 by Daniel Mark, Statistical Mech. 1 & 2 by Kien Pham, EM 1 & 2 by Michael Reefe, QM 1 & 2 by Zhaoyi Li****2016 Spring**: Exam | Solution**2015 Fall**: Exam | Solution**2012 Fall**: Exam | Solution [Correction to E&M Q1c by Abdelaziz Hussein]**2012 Spring**: Exam | Solution**2002 Fall**: Exam | Solution [Correction to E&M Q1 by Wenzer Qin]**2002 Spring**: Exam | Solution [Student contributions:**all problems**by Istvan Cziegler; corrections to Stat Mech Problem 1 and Problem 2 by Anthony Grebe]**2001 Fall**: Exam | Solution**2001 Spring**: Exam | Solution**2000 Fall**: Exam | Solution**2000 Spring**: Exam | Solution [Student contributions:**CM 1 & 2 by**by Mingyu Charles Li]**1999 Fall**: Exam | Solution**1999 Spring**: Exam | Solution**1998 Fall**: Exam | Solution [Student contributions:**QM 1 & 2**by Leo Stein;**CM 1**by Koushik Balasubramanian;**CM 2**by Vijay Kumar Sreenivasa Gopalan;**E&M 1**by Eric Fitzgerald]**1998 Spring**: Exam | Solution**1997 Fall**: Exam | Solution

**Oral Exam Study Guide**

**The MIT Physics GSC hosts a wiki site for topics and questions that appeared in past oral exams (known as "Part III" prior to 2015). In addition, Brian Ross has generously compiled a study guide in 2008 for biophysics. We welcome simlilar compilations for other divisions!**