Studying for the exam or for learning? Is there time later?

Question

I don't know if there's a correct answer to my dilemma, but I'd like the opinion of other people, in and outside the field, maybe older and more "experienced in life" than me. This is my situation

I am a graduate student in theoretical physics, I started my undergraduate courses in an extremely humble way, looking at professors and physicists in general as some kind of superhumans I would have been unable to match. Thus my only intent was to exploit them and get from them as much knowledge as I could, before coming back home and looking for a job, even totally unrelated with physics. So I always studied for passion, taking exams just to be able to be get the degree and then follow graduate courses to extort more knowledge to the professor. Without taking the degree my parents wouldn't have allowed me to stay here with no "tangible results" while receiving their financial help, so I couldn't just follow lectures and study without doing exams.

During the years I kept studying for passion, the results at the exams where excellent and I started considering the fact that maybe I wasn't that bad. Then I started to get closer and closer to professors and assistants, and my view of them changed, they became mere mortals, I thought I could fit there and actually become one them one day, maybe not a great one, but still a person who can be properly called a physicist.

That's the birth of my problem: I decided I can become one of them, I still know quite a lot excellences that I think I can't reach but I can definitely be an average guy in the field, in my mind that's a fact now, and I want to be that guy.

This semester I started graduate school. To stay in the field after it, you have to keep the highest marks and all sort of things in order to get the PhD and to keep working with people better than you who can teach you and make you a better scientist.

This is changing the way I study, I started studying for the exams, and not in the free and careless way I used to do before. A problem is that in Theoretical physics there are a lot of different approaches, styles, conventions and notations to do the same stuff. Two years ago I would have taken 3-4 very good books, my notes from lessons and then I would have mastered the subject in the best possible way for my level. At this point I would have taken the exam mainly careless of the mark, especially if positive. A negative one is a sign you probably didn't master the subject at least at the level required, so I would have cared about it.

That's what I'd like to do now, but I have to be realistic, graduate school is a little bit harder (at least for me) and doing that would require me a lot more time than it used before, slowing down the pace at which I take exams and making me finish graduate school later. But now I suppose I have to care about the exams and taking them as soon as I can. And if doing as I always did I don't master the subject good enough to take the highest marks? I could have prepared that exam in less time just focusing on it and take the good mark that would allow me, in future, to stay in the field.

I have a lot anxiety for the upcoming exams, they never scared me, but now they do.

I don't like the situation, but should I maybe just accept it, swallow the bitter bill, study just for the exams, stay in the field, getting the Phd, and then and only then studying what I want more freely?

In a line: Time and marks has never been a problem for me, now they are a burden.

PS: I don't consider myself able to do decent research on my own staying out of the academic world, far from better minds I can get help from, so studying just for me and then doing my own research isn't an option here.

Answer 1

In my experience (which has been both as a student and a professor), the best way to do well in theoretical physics graduate school is to get a really good understanding of the material. That will give you the best path forward. If you try to memorize a bunch of recipes for solving all different kinds of exam problems, you are missing the forest for the trees. Moreover, once you are done with courses and exams, you will need to put what you have learned to use in a research context. In doing research, it's how well you really understand the underlying physics that is going to matter the most.

To solve particular problems in E&M or quantum mechanics, you may learn a lot of mathematical techniques, which can seem unrelated or disconnected at first. However, many of them are really variations on the same underlying methodology. For example, the solution of the Schroedinger equation using energy eigenstates is really a form of separation of variables, like that used in E&M. Similarly, separation of variables in spherical coordinates is really the same as a multipole expansion. The best way to see these connections is to work examples problems, and most good textbooks at the graduate level have problems that are specifically designed to illustrate the deeper connections between the different techniques you have learned.

So my advice to you (and to the students I teach) is to go for deeper understanding of the physics and why certain strategies work in certain situations. If you master that, you will also learn how to apply various techniques as a necessary corollary.