I have decided to tackle this issue because it became a very common question in many physics forums. Can someone, without a degree in physics, get accepted and succeed in physics graduate school all the way to obtaining a Ph.D?
Obviously, this question cannot be answered easily, because it depends on (i) your major (ii) what physics and mathematics classes you took as an undergraduate. Students majoring in, say electrical engineering, engineering mechanics, mathematics, applied mathematics, etc. will have an easier path to going into physics than, say, student who majored in economics, musics, etc., mainly because of many overlap in courses that one took as an undergraduate.
Still, I think that there is a concrete way to determine how well-prepared you are in going into a physics graduate program. This is something you can do yourself as a first level of self-evaluation on whether you are well-equipped to enter such program, or if you lack some necessary knowledge to complete it successfully.
1. Get a copy of a GRE Physics Subject test. Now try to do the test yourself. If you did not score 75% or better, you lack the necessary preparation to go into a physics graduate school
2. If you have a school that you already have in mind on where you might want to apply to, get a copy of the previous-year’s qualifying exams (more on the qualifying exams in Part IX of this essay). You don’t even have to actually do the exam. Just read it, and see if you actually understand what it is asking, and what you will need to be able to solve it. If you find that there are questions that go over your head, and you don’t know where to look for the way to start solving it, you immediately lack the necessary preparation to go into a physics graduate school.
These are concrete, self-evaluation that you can test on yourself. The GRE self-test should test a wide variety of physics knowledge that a typical physics undergraduate should have by the time he/she graduates. This allows you to compare your knowledge to such group of student. 75th percentile score isn’t that high, but in this self-test, you get to use as much time as you need, and may even need to refer to physics text books to help you with your test (something you can’t do in an actual GRE test). I consider knowing where to look for help as an indication that a student isn’t clueless.
The qualifying exam self-test is more school-specific. This is the standard of knowledge that a particular school would want their graduate candidates to have, so the questions tend to be more difficult, and it isn’t a multiple choice exam. Here, I merely wanted you to see if you can actually understand what is being asked, and then to know a way to solve it, without actually having to solve it. Most physics students can understanding the question, and have an idea on how to solve it. The process of solving the question itself may not be trivial (usually, it isn’t!), but knowing a way to do it is a major indication that a student has the necessary knowledge. So if you encounter anything here that makes no sense to you, and you also are clueless in figuring out a way to solve it, then you lack the necessary preparation.
The thing here is that, depending on where you intend on applying and your educational background, getting accepted into a physics graduate program isn’t the biggest issue, especially if you’re paying the full tuition and fees yourself. With an engineering degree/computer science/math degree and a GAP of 3.0 or better, you can find schools that might accept you into their program. The question is, can you survive in the program and ultimately, get to your goal of receiving your Ph.D? It would be a waste of time (and financial resources if you’re paying full fare) if you get snagged in the qualifying exams because you were not sufficiently prepared.
If you don’t think you are sufficiently prepared, you need to evaluate on whether you should apply to a school, and then spend maybe a year, or even two, in advanced undergraduate courses to not only get you up-to-speed, but also to prepare you for the qualifying exams. Many schools will allow you to do this. This evaluation will depend on your current educational background. I would say that engineering and math majors will have the advantage here on not needing way too many courses to get them up and running. If you come from a non-science, non-technical background, you may want to consider how far up a hole you’re willing to climb to achieve your goal.
Using the two self-tests that I mentioned above will give you a concrete evaluation of your knowledge to survive a physics graduate program.