Notes for the Physics GRE
Tom Rudelius
Harvard University
,Contents
1 Introduction 2
2 General Advice 2
3 Classical Mechanics (20%) 3
4 Electromagnetism (18%) 6
5 Optics and Waves (9%) 17
6 Thermodynamics and Statistical Mechanics (10%) 24
7 Quantum Mechanics (12%) 29
8 Atomic Physics (10%) 36
9 Special Relativity (6%) 39
10 Miscellaneous (15%) 40
1
,1 Introduction
Hello, potential physics Ph.D. student! If you are reading these notes, chances
are you are preparing to take the physics GRE subject test (pGRE). This exam,
administered by the Educational Testing Service (ETS), consists of 100 multiple
choice problems in 170 minutes. Students score one point for every correct
answer and lose a quarter of a point for every incorrect answer, so arbitrary
guessing is costly. The raw score out of 100 is converted to a scaled score out of
990, which roughly corresponds to a raw score of 85 or above and a percentile
of 95.
The test is designed to measure the student’s physical intuition and educa-
tion, but in practice it also measures a student’s calculation speed: most stu-
dents who take the test are unable to complete it in the time allowed. Hence,
you do not want to have to waste time on the exam re-deriving formulas and
should try to commit as much of your undergraduate physics education to mem-
ory as possible. In these notes, I will present some of the most prolific formulas
found on the pGRE, along with some general tips for taking the exam. The rest
is in your hands. Good luck!
2 General Advice
These are the best tips I can give to someone preparing for the pGRE.
1. Take the test seriously. ETS isn’t going to give you any extra points
because the name of your undergraduate institution is “Harvard,” “Stan-
ford,” “MIT,” “Princeton,” “Cornell,” etc. The test might not be as dif-
ficult or rigorous as the exams you’re accustomed to, but taking it lightly
is a big mistake (and one that some of the smartest and most talented
undergrads make every year). The pGRE is probably about as important
as the rest of the exams you’ve taken in your undergraduate career com-
bined: treat it as such. If you want to study theoretical physics at one of
these top schools, you should probably shoot for a score of 900 or better.
2. Take every available practice exam, and do so under testing con-
ditions. ETS should mail you a practice booklet when you register for
the pGRE, and you can find a set of four other practice tests on the Ohio
State Physics web page. You should take all five of these exams under
testing conditions (i.e. in 170 minute intervals). As Vince Lombardi said,
“Practice does not make perfect. Only perfect practice makes perfect.”
Don’t waste your time by doing a few practice problems here and there:
approach the practice test in the same manner you approach the real test,
and get accustomed to 170 minutes of furious thought.
3. Start studying early. I started studying for the October physics GRE
subject test the day that I finished the math GRE subject test in April.
This is probably a tad extreme, but you should probably start studying
2
, at least 2 months before the exam. A good strategy would be to take the
first practice test 2 months before the exam to get an idea of what you
need to learn, the second practice test 1 month before the exam, the third
2 weeks before the exam, the fourth 1 week before the exam, and the fifth
2 days before the exam.
4. Set a consistent sleep schedule of at least 8-9 hours per night.
Anyone who has taken Psych 101 at Cornell with Professor James Maas
can tell you that the average undergrad needs 9.25 hours of sleep per night
to be well-rested. Furthermore, it is critical to develop a consistent sleep
schedule. This can be a problem for many aspiring physics grad students
because the pGRE is administered at 8:30am, so you will probably have
to wake up at 7:30am or so. For the week before the exam, you should
really try to get on an 11pm to 7:30am sleep schedule (as tough as that
might be for a physics party animal such as yourself). Whatever you do,
don’t stay up late studying for the exam.
5. Take your own, handwritten notes. Actually writing formulas down
improves your ability to remember them. While the notes presented here
are nice as a guide, you should create your own notes, even if they are just
paraphrases of mine.
6. Use dimensional analysis. A decent fraction of the problems on the
pGRE can be solved using dimensional analysis. Before starting a 5-
minute calculation, pause to see if you can determine the answer based
solely on its dimensionality.
3 Classical Mechanics (20%)
Newton’s laws:
F = ma, (1)
F12 = −F21 . (2)
Newton’s gravitational law:
GM m
F~ = r̂ (3)
r2
where r is the distance between two objects of mass M and m, respectively, and
−2
G is the gravitational constant. On earth, g = GM
r 2 = 9.8m · s . Kepler’s laws
of planetary motion:
1. The orbit of every planet is an ellipse with the Sun at one of the two foci.
2. A line joining a planet and the Sun sweeps out equal areas during equal
intervals of time.
3
Tom Rudelius
Harvard University
,Contents
1 Introduction 2
2 General Advice 2
3 Classical Mechanics (20%) 3
4 Electromagnetism (18%) 6
5 Optics and Waves (9%) 17
6 Thermodynamics and Statistical Mechanics (10%) 24
7 Quantum Mechanics (12%) 29
8 Atomic Physics (10%) 36
9 Special Relativity (6%) 39
10 Miscellaneous (15%) 40
1
,1 Introduction
Hello, potential physics Ph.D. student! If you are reading these notes, chances
are you are preparing to take the physics GRE subject test (pGRE). This exam,
administered by the Educational Testing Service (ETS), consists of 100 multiple
choice problems in 170 minutes. Students score one point for every correct
answer and lose a quarter of a point for every incorrect answer, so arbitrary
guessing is costly. The raw score out of 100 is converted to a scaled score out of
990, which roughly corresponds to a raw score of 85 or above and a percentile
of 95.
The test is designed to measure the student’s physical intuition and educa-
tion, but in practice it also measures a student’s calculation speed: most stu-
dents who take the test are unable to complete it in the time allowed. Hence,
you do not want to have to waste time on the exam re-deriving formulas and
should try to commit as much of your undergraduate physics education to mem-
ory as possible. In these notes, I will present some of the most prolific formulas
found on the pGRE, along with some general tips for taking the exam. The rest
is in your hands. Good luck!
2 General Advice
These are the best tips I can give to someone preparing for the pGRE.
1. Take the test seriously. ETS isn’t going to give you any extra points
because the name of your undergraduate institution is “Harvard,” “Stan-
ford,” “MIT,” “Princeton,” “Cornell,” etc. The test might not be as dif-
ficult or rigorous as the exams you’re accustomed to, but taking it lightly
is a big mistake (and one that some of the smartest and most talented
undergrads make every year). The pGRE is probably about as important
as the rest of the exams you’ve taken in your undergraduate career com-
bined: treat it as such. If you want to study theoretical physics at one of
these top schools, you should probably shoot for a score of 900 or better.
2. Take every available practice exam, and do so under testing con-
ditions. ETS should mail you a practice booklet when you register for
the pGRE, and you can find a set of four other practice tests on the Ohio
State Physics web page. You should take all five of these exams under
testing conditions (i.e. in 170 minute intervals). As Vince Lombardi said,
“Practice does not make perfect. Only perfect practice makes perfect.”
Don’t waste your time by doing a few practice problems here and there:
approach the practice test in the same manner you approach the real test,
and get accustomed to 170 minutes of furious thought.
3. Start studying early. I started studying for the October physics GRE
subject test the day that I finished the math GRE subject test in April.
This is probably a tad extreme, but you should probably start studying
2
, at least 2 months before the exam. A good strategy would be to take the
first practice test 2 months before the exam to get an idea of what you
need to learn, the second practice test 1 month before the exam, the third
2 weeks before the exam, the fourth 1 week before the exam, and the fifth
2 days before the exam.
4. Set a consistent sleep schedule of at least 8-9 hours per night.
Anyone who has taken Psych 101 at Cornell with Professor James Maas
can tell you that the average undergrad needs 9.25 hours of sleep per night
to be well-rested. Furthermore, it is critical to develop a consistent sleep
schedule. This can be a problem for many aspiring physics grad students
because the pGRE is administered at 8:30am, so you will probably have
to wake up at 7:30am or so. For the week before the exam, you should
really try to get on an 11pm to 7:30am sleep schedule (as tough as that
might be for a physics party animal such as yourself). Whatever you do,
don’t stay up late studying for the exam.
5. Take your own, handwritten notes. Actually writing formulas down
improves your ability to remember them. While the notes presented here
are nice as a guide, you should create your own notes, even if they are just
paraphrases of mine.
6. Use dimensional analysis. A decent fraction of the problems on the
pGRE can be solved using dimensional analysis. Before starting a 5-
minute calculation, pause to see if you can determine the answer based
solely on its dimensionality.
3 Classical Mechanics (20%)
Newton’s laws:
F = ma, (1)
F12 = −F21 . (2)
Newton’s gravitational law:
GM m
F~ = r̂ (3)
r2
where r is the distance between two objects of mass M and m, respectively, and
−2
G is the gravitational constant. On earth, g = GM
r 2 = 9.8m · s . Kepler’s laws
of planetary motion:
1. The orbit of every planet is an ellipse with the Sun at one of the two foci.
2. A line joining a planet and the Sun sweeps out equal areas during equal
intervals of time.
3
