Graduate School

Graduate school in physics or related fields generally refers to a post-baccalaureate education sequence where a student earns their doctorate degree, or Ph.D. Unlike a baccalaureate whose requirements primarily focus on classes, Ph.D. programs focus on an original research contribution in the form of a written thesis and typically defense in front of a committee.

Because of the heavy research focus, you should only ever go to graduate school if you enjoy doing research. It is by no means the necessary "next step" (certainly not in comparison to the transition from high school to college, which is a more common and broadly applicable path). While it is true that, in many cases, Ph.D. holders make slightly more money in industry, it is also true that Ph.D. students forego ~5-6 or more years of working in private industry, and thus any promotions or experience associated therewith. That being said, grad school is the next step if you are planning a future career in academia.

Note that grad school does not have to follow directly after undergrad; many people first go to industry for a number of years before deciding to return to grad school, and many of these people go on to take up permanent positions in academia.

It is important to keep in mind that any Ph.D. program worth your while will pay you to go. While there is technically a tuition, the school will almost always cover this, and allot you a stipend anywhere between $13,000 to $34,000 or even more annually. This is because, as a salaried researcher, you are actually contributing value to the university in the form of original research and teaching responsibilities.

Preparing for the Application

Students who go to graduate school straight out of undergrad typically apply to grad school during their senior (fourth) year, first (fall) semester, though some students choose to take a gap year to either do external research, finish up projects, or travel.

While requirements vary, typically grad school in physics (and often related fields such as astrophysics) will require:

• One or more research/purpose/diversity statements
• A score on the Graduate Record Exam (GRE)
• A score on the GRE Physics Subject Test (PGRE)
• Three letters of recommendation

Writing a Statement of Purpose

When writing a statement of purpose to a graduate school, it helps to think about the following questions:

• Why am I applying to graduate school?
• What kind of research have I done in the past, and how does this research prepare me for graduate study?
• What about the specific program I am applying to is appealing to me?
• Who would I want to work with if I went to this school?

All of these questions are immensely important to include in a statement of purpose. Successful grad school applicants typically communicate their enthusiasm for research, extensive past research experience (and deliverables such as papers, talks, and posters), and a number of faculty with whom they would like to work.

Believe it or not, graduate programs are immensely different, and it is extremely valid (and common) to choose a graduate school based off of the faculty who are there. As you reach this point in your academic career, you will realize that, oftentimes, even top schools may lack researchers in your specific field, and you should take this into account. Moreover, it pays to verify directly with potential research advisors whether or not they plan on taking graduate students, and what kind of advising style they have (e.g., hands-off, hands-on). It is also beneficial to keep in mind other nearby institutions with which your prospective school frequently interacts.

Some examples are below:

• California Institute of Technology: Carnegie Observatories
• Columbia University: Flatiron Institute
• Princeton University: Institute of Advanced Study
• University of Chicago: Kavli Institute for Cosmological Physics
• University of California, Berkeley: Lawrence-Berkeley National Laboratory
• Stanford University: SLAC National Accelerator Laboratory
• University of California, Santa Barbara: Kavli Institute for Theoretical Physics
• University of Hawaii at Manoa: Keck Observatory

One common mistake that students make when writing statements of purpose is subconsciously implementing self-deprecating language. This may take an explicit form: "Even though I don't know much about...," but can often take more subtle forms:

• "My research advisor assigned me to ..." - You want to sound directed in your research. While it may be true that you did work assigned by your advisor, the graduate admissions committee what to know what about what you, not your advisor, did.
• "I characterized growths and ran code to fit spectra." - This sort of language is a mistake because, rather than focusing on the day-to-day mechanical applications of what you are doing, you should show some perspective in why what you're doing is interesting. You should make big-picture statements about the motivation of your project, and what you specifically tried to learn and what the outcome was.
• "I learned a lot." - About what? Talking about what you have learned can be extremely helpful, but you should be concrete about this.

If you have a paper (not necessarily first- or even high author position), poster, or presentation, you should absolutely mention this in your statement of purpose, even if it appears in your curriculum vitae (~resume). It will help convince people that you have had exposure to the actual process of doing research, and are thus likely to succeed in grad school.

Even students who go to top schools experience imposter syndrome, but bearing this fact in mind should convince you that writing confidently can only help you, and is not "dishonest," even if you feel like you still have a lot to learn.

Graduate Record Examination (GRE)

The Graduate Record Examination (GRE) is a standardized examination either conducted on paper or administered via a computer at a specialized facility. It has three parts, a "verbal reasoning" language section (scored 130-170), a "quantitative reasoning" mathematics section (scored 130-170), and an "analytical writing" essay section (scored 0-6). The GRE is administered by the ETS corporation and is taken by basically all students in the United States applying to graduate school in any subject. As such, it is extremely general knowledge which is comparable to the standard SAT/ACT in difficulty and content. This being said, you should be able to take the GRE basically as early in your college experience as you would like, though it is typical for students to take it during the same semester that they are applying for grad school.

Graduate Record Examination, Physics Subject Test (PGRE)

The Graduate Record Examination, Physics Subject Test (PGRE) is a standardized examination typically taken on paper on the contents of a typical physics undergraduate curriculum, and is graded from 200-990 in increments of 10 points. The score on the PGRE is slightly more important than that of the standard GRE. It is a 2 hour and 50 minute multiple choice exam with ~100 questions. According to ETS, the breakdown of the content of the exam is as follows:

• CLASSICAL MECHANICS — 20% (such as kinematics, Newton's laws, work and energy, oscillatory motion, rotational motion about a fixed axis, dynamics of systems of particles, central forces and celestial mechanics, three-dimensional particle dynamics, Lagrangian and Hamiltonian formalism, noninertial reference frames, elementary topics in fluid dynamics)
• ELECTROMAGNETISM — 18% (such as electrostatics, currents and DC circuits, magnetic fields in free space, Lorentz force, induction, Maxwell's equations and their applications, electromagnetic waves, AC circuits, magnetic and electric fields in matter)
• OPTICS AND WAVE PHENOMENA — 9% (such as wave properties, superposition, interference, diffraction, geometrical optics, polarization, Doppler effect)
• THERMODYNAMICS AND STATISTICAL MECHANICS — 10% (such as the laws of thermodynamics, thermodynamic processes, equations of state, ideal gases, kinetic theory, ensembles, statistical concepts and calculation of thermodynamic quantities, thermal expansion and heat transfer)
• QUANTUM MECHANICS — 12%(such as fundamental concepts, solutions of the Schrödinger equation (including square wells, harmonic oscillators, and hydrogenic atoms), spin, angular momentum, wave function symmetry, elementary perturbation theory)
• ATOMIC PHYSICS — 10% (such as properties of electrons, Bohr model, energy quantization, atomic structure, atomic spectra, selection rules, black-body radiation, x-rays, atoms in electric and magnetic fields)
• SPECIAL RELATIVITY — 6% (such as introductory concepts, time dilation, length contraction, simultaneity, energy and momentum, four-vectors and Lorentz transformation, velocity addition)
• LABORATORY METHODS — 6% (such as data and error analysis, electronics, instrumentation, radiation detection, counting statistics, interaction of charged particles with matter, lasers and optical interferometers, dimensional analysis, fundamental applications of probability and statistics)
• SPECIALIZED TOPICS — 9% Nuclear and Particle physics (e.g., nuclear properties, radioactive decay, fission and fusion, reactions, fundamental properties of elementary particles), Condensed Matter (e.g., crystal structure, x-ray diffraction, thermal properties, electron theory of metals, semiconductors, superconductors), Miscellaneous (e.g., astrophysics, mathematical methods, computer applications)

Note that some programs have been gradually phasing out GRE/PGRE requirements, but this is still a minority of programs and it is, in the vast majority of cases, better to take this exam if you have the ability. While there are ~5 publicly released PGRE exams with scoring guidelines, the general scoring formula depends from session to session and is propriety on behalf of ETS (and thus private). While there are other practice examinations on the internet, they do not have officially sanctioned scoring assignments. Hence, when studying for the PGRE, it is better to take the official exams only when you feel ready to get an accurate score estimate, because of the limited number available.

The current iteration of the PGRE does not penalize for wrong answers (which is not true of all of the practice exams), so it is in your advantage to fill out an answer on every question, even if it is a guess. It is not necessary at all to get all the questions right in order to get a good (or even perfect) score. It may feel at times like you are making barely educated guesses on most questions, but you should persevere, as this is a common feeling.

Letters of Recommendation

Most grad programs require three letters of recommendation. A letter of recommendation is a private statement made on behalf of somebody who knows you to an institution to which you are applying, stating your preparation for the program and their positive research/personal experiences with you. In order to optimize your chances of getting into a good graduate school, it is in your best interest to make as many of your three/four recommenders people with Ph.D's (professors, postdocs) who know you personally and have worked with you in a research context. In the event that this is not possible, you should ask for letters of recommendation from professors of classes in which you have done well, and who know you relatively well (e.g., from office hours, etc.). Do not get a letter of recommendation from somebody who does not like you.

In an optimal case, you should ask your recommenders ~1 month or more in advance for letters of recommendation, and it often pays to also provide excerpts of your statement of purpose. It is a good idea to share to them some kind of online spreadsheet of all places which require a letter of recommendation, complete with links to submit the letter of recommendation/email addresses to send them, etc. as well as deadlines, and clear indications of whether or not this task has been complete.

FERPA is a regulation in the United States giving you the right to see your letter of recommendation, and schools will typically ask you whether or not you would like to waive this right. You should always opt to waive your rights to see your letter of recommendation, as schools typically know whether or not you have done so. Letters for which you have not waived your FERPA right may treat your letter of recommendation with more skepticism, as they know that your letter writer may not feel comfortable to speak completely honestly about their experiences with you.

Applying for External Fellowships

External fellowships are sources of funding outside of the graduate school which you go to. It doesn't cost anything to apply to a fellowship; even though it may feel like a lot of work, it is generally worth it for a number of reasons:

• Your graduate stipend may be increased (this is not always the case)
• Because the tuition burden on the department you are going to is lessened, the department is more eager to attract you (you can even reverse a rejection decision from a school by telling them you have obtained a fellowship)
• Since you come into graduate school with your own funding, you are not prevented from working with certain professors who may not have funding, and will not be bound to work for projects you find uninteresting because some grant is contingent upon it
• You will not be made to TA in order to earn your stipend

Fellowships all have their individualized purposes, and you should write your statements for these fellowships bearing in mind what the fellowship is actually for. Below is a non-exhaustive list of fellowships that you should consider applying to:

• National Science Foundation Graduate Research Fellowship (NSF-GRFP): Funded by the National Science Foundation, for students with demonstrable "intellectual merit" (research accomplishments) and "broader impact" (outreach). Applicants write a personal statement and a research proposal to which they are not bound (as the NSF-GRFP funds people mostly regardless of change in career plans).
• National Defense Science and Engineering Graduate Fellowship (NDSEG): Funded by the Department of Defense, and for projects which have some demonstrable significance, direct or indirect, to national defense
• Ford Foundation Fellowship: Aims to train future researchers devoted to education and diversity
• Computer Science Graduate Fellowship (CSGF): Funded by the Department of Energy, for researchers who plan to do computationally heavy work. Acceptance of this fellowship requires the school to agree not to require more than a certain number of TA semesters. It is also contingent upon the completion of a number of graduate courses in a number of fields for broad training.
• Hertz Foundation Fellowship: An extremely competitive private fellowship emphasizing creativity and patriotism, lengthy process involving an initial application followed by two in-person interviews selecting ~12 students per year in all fields.

If you have the fortune of obtaining multiple fellowships, you should take care of figuring out how the fellowships interact, and how they interact with the funding at your home institution. Whether or not you can accept certain fellowships may also depend on the institution to which you are applying, and also whether or not it is abroad. US government fellowships are not typically available to international students.

Visiting and Choosing Graduate Schools

If you are accepted to a graduate school, typically the graduate school will fund a visit on your behalf to their school in an open house. In the event that you cannot make the time that they scheduled, they are generally willing to accommodate a separate time, and will often construct personalized itineraries just for you.

During this visit, a couple of things will generally happen:

• You will be scheduled with a large number of short meetings with many faculty, including the faculty that you specified you wanted to work with on your application
• You will spend a day or a couple of days within the department, meeting current graduate students and other relevant people
• You will be given a lot of very nice food and put in a very nice hotel, and people will act unnaturally nice to you for about a month

Some things you should keep in mind. You should feel free to talk about these points openly, since people are generally understanding that you are trying to make the best decision for yourself, and are trying to get as much information as possible:

• Do not go to a place where you have nobody you are excited to work for, and be hesitant to go to a place where there is only one such person (as the advising fit may go bad for any number of reasons).
• Talk to graduate students, both current ones and those who have dropped out, if you can locate them. They tend to be extremely honest about their experiences, and will generally not hesitate to tell you red flags about a school or potential advisor. If a school or advisor seems to be discouraging you from talking to someone, that is a huge red flag.
• Do you actually see yourself living in the location of the school? This sounds like it wouldn't be that important, but it totally is, because this is where you're spending the next half decade of some of the best years of your life.
• Is your advisor of interest actually taking students? Can they commit to taking you?
• What is the funding situation like? Do students tend to have enough travel funds to go to conferences, etc.

Graduate visits are extremely exhausting since your schedule is often booked completely, so if you are accepted to many places, be honest about which schools you are actually considering. Graduate schools across the country have unanimously decided that April 15th is the deadline to accept or reject a graduate school decision, and you should not hold out later than this for any US grad school you are hoping will admit you off of a waitlist.

Graduate School Abroad

While graduate school abroad can often be very rewarding, there are a lot of significant differences between US grad schools and international grad schools. Some of the big points are below:

• Many fellowships (in particular, government fellowships) do not apply if you go to a school abroad
• In US grad schools, students apply directly to a Ph.D. program where they earn an ancillary masters degree. However, in programs abroad, these are typically two separate programs, with Ph.D. candidates doing a masters program before their doctorate
• Ph.D. programs abroad (especially in Europe) tend to be shorter (~3 years) and are sometimes regarded as being less comprehensive