Applying to top schools -- What do they look for?

[Squark123]

I am applying to graduate schools in physics. I studied physics independently when I was doing a challenging B.Sc degree. Despite taking no mathematics and physics courses, my studies enabled me to score highly in the physics GRE and to succeed in several theoretical physics graduate courses. I did not do research in the sense of doing some original calculation which is worthy of publication. But I did study subjects, such as quantum field theory and algebraic topology on my own. I am writing this because I would like to apply to top schools. However, I am reluctant to do so because they look for strong research experience, like for instance working under some supervisor doing some calculation/simulation. I did not produce any new knowledge. Will this self-study convince the admission committees at ,say top 20, schools to choose me? My scores in the graduate physics courses are good (As and B) For instance, I earned an A in an electrodynamics course taught from Jackson. Will this be sufficient?

 

[Choppy]

Despite taking no mathematics and physics courses,

This will likely be a problem. Even having taken and done well in graduate courses, there may be a question as to whether you have the appropriate background. That said, I suppose a lot depends on what your undergraduate program did include. A challenging engineering program with good marks in graduate physics courses will likely make you competitive. An arts major who somehow managed to get learn enough E&M to do well in a first year graduate class, perhaps less so.

Self-study doesn't count for much. It's great that you did it, but anyone can claim to have self-studied anything. There's very little objective validation until you go through some kind of formal assessment, i.e. taking a class.

With respect to research experience, competitive programs are generally looking for some evidence that you'll be able to thrive doing research. In that respect they're looking at summer positions, volunteer work, fourth year thesis projects, even projects that you've been involved with as part of a student group (makers club, robotics team, etc.) Some people have this notion that you need to have N first-author publications as an undergrad, but I don't think that's really the case. Sure, it can help, but most people in the game are also aware that when an undergrad ends up on a publication it's often because that student was fortunate enough to have a strong mentor. In short, they're looking for people who have made the best of the opportunties they've had, not necessarily those who've had the best opportunities.

 

[Squark123]

I studied medicine. I performed well in medicine. The courses I have taken in the graduate program are: classical mechanics, electrodynamics, quantum mechanics, mathematical physics and quantum field theory. I performed well in them despite the fact that I had not taken the undergrad versions of it. Regarding research, I am doing a fellowship but I am still starting. So, I can't provide recommendation letters talking about my research potential. Fourth year projects at my school just involves studying some well-understood topic and making a thesis out of it. I did something similar; I also studied well-known topics.

club, robotics team, etc.) Some people have this notion that you need to have N first-author publications as an undergrad, but I don't think that's really the case. Sure, it can help, but most people in the game are also aware that when an undergrad ends up on a publication it's often because that student was fortunate enough to have a strong mentor. In short, they're looking for people who have made the best of the opportunties they've had, not necessarily those who've had the best opportunities.

 

[PeroK]

I studied medicine. I performed well in medicine. The courses I have taken in the graduate program are: classical mechanics, electrodynamics, quantum mechanics, mathematical physics and quantum field theory. I performed well in them despite the fact that I had not taken the undergrad versions of it. Regarding research, I am doing a fellowship but I am still starting. So, I can't provide recommendation letters talking about my research potential. Fourth year projects at my school just involves studying some well-understood topic and making a thesis out of it. I did something similar; I also studied well-known topics.

I'm fascinated by this. You say you have studied QM and QFT. Just out of interest, can you help this guy out?

https://www.physicsforums.com/threads/degeneracy-of-hydrogen-energy-levels.981678/

Just to get a handle on what you do know about QM.

 

[Squark123]

Let me think about it. The Energy eigenstates should be a solution of the associated legendre equation multiplied by $e^im\phi$ multiplied by a solution of the radial equation. Right? We can't do anything to the $e^im\phi$ or the radial part, I believe. Now, consider the solutions to the associated legendre function. We want it to vanish at $\theta=\pi/2$. Right? This means that the solution should have a cos(\theta) in it. Also, it should be linear in cos(\theta). Y_{2}^{-1} and Y_{2}^{+1} satisfies this, so they vanish at $\theta=\pi/2$. Y_{2}^{0} does not satisfy it so it can't satisfy the boundary conditions. Note that the superscript is the $m$ and the subscript is the $\ell$. I did not calculate what all the allowed $m$ and $\ell$ are. To do that, I have to have a paper because I don't exactly remember the spherical harmonics. Does my analysis make sense so far?

 

[PeroK]

Let me think about it. The Energy eigenstates should be a solution of the associated legendre equation multiplied by $e^im\phi$ multiplied by a solution of the radial equation. Right? We can't do anything to the $e^im\phi$ or the radial part, I believe. Now, consider the solutions to the associated legendre function. We want it to vanish at $\theta=\pi/2$. Right? This means that the solution should have a cos(\theta) in it. Also, it should be linear in cos(\theta). Y_{2}^{-1} and Y_{2}^{+1} satisfies this, so they vanish at $\theta=\pi/2$. Y_{2}^{0} does not satisfy it so it can't satisfy the boundary conditions. Note that the superscript is the $m$ and the subscript is the $\ell$. I did not calculate what all the allowed $m$ and $\ell$ are. To do that, I have to have a paper because I don't exactly remember the spherical harmonics. Does my analysis make sense so far?

Okay, so you're not delusional! You really do understand QM!

 

[Squark123]

Thank you. By the way, the examples that I have given above that satisfy the correct boundary conditionssatisfy the condition that $m^2-l(l+1)$ is an odd integer. Can you check that this is the required relation? I think one can start with the associated legendre equation and put sin(\theta)=1 and solve. In this case, I think you might get that condition.

 

[PeroK]

Thank you. By the way, the examples that I have given above that satisfy the correct boundary conditionssatisfy the condition that $m^2-l(l+1)$ is an odd integer. Can you check that this is the required relation? I think one can start with the associated legendre equation and put sin(\theta)=1 and solve. In this case, I think you might get that condition.

I don't want to hijack your thread. If I could help him I would have. The problem says $x < 0$, which makes no sense to me. Maybe it should be only at $x = 0$, but then that is right through the nucleus. I have no ideas!

 

[romsofia]

I'm happy you're pursuing you passion, but keep in mind that an A in a graduate course isn't the same as an A in a undergraduate course. That being said, if you have them on your transcripts, then apply! You have a unique application which we can't judge fully. If i were in your shoes I'd do the following:
1) Go to arxiv.org, pick the field you (potentially) want to do research in, and read some papers that interest you.
2) Look at where the papers are coming from, check out the university and what their guidelines are for graduate admission.
3) Believe in yourself, and apply.

 

[Vanadium 50]

We've been through this before.

Your GRE score is such that about 1000 applicants are ahead of you. I'm not sure the top 20 programs even enroll 1000 students. And that's where you are doing best. We went over this last time, but with no undergraduate degree in physics and an RA where the professor is unwilling to write you a letter, there are a lot of red flags.

That was last year. What's changed since then?

 

[Squark123]

What changed is that I can provide a transcript. It is not that a professor is unwilling to write me a letter. I spent some time (the period I was working as a research assistant) working by myself in an area (QFT) which is not the area of the expertise of the PI. Keep in mind that I don't live in US or Europe. If I were, I would not be asking this question because I would have found someone who is knowledgeable enough to work with.

 

[StatGuy2000]

What changed is that I can provide a transcript. It is not that a professor is unwilling to write me a letter. I spent some time (the period I was working as a research assistant) working by myself in an area (QFT) which is not the area of the expertise of the PI. Keep in mind that I don't live in US or Europe. If I were, I would not be asking this question because I would have found someone who is knowledgeable enough to work with.

It may help the people on this thread to know where you are from, as this may help to determine what are your prospects in applying for graduate programs in physics.

 

[Squark123]

I am from Egypt.

 

[DEvens]

It's not impossible. It's not the usual path, but it's not impossible. Usually what it will take is to attract the positive attention of some "big name" at one of the schools. That person's recommendation will carry a lot of weight. It will help if you have studied something relevant to the research work of at least one prof at a school you would like to go to. You may have success by contact that prof directly. You may get hints on who to contact by looking at arxiv.org for papers in areas you are interested in.

Two anecdotes, for what they are worth.

In my grad program, one of the other students under the same prof had an undergrad degree in languages. For fun he would get the Chinese student newspaper and read it at lunch. It was Cantonese in traditional Chinese characters. Not even simplified characters, the ones that I have learned to know about 30 of. He took very little math and physics in undergrad, being busy with learning four languages. But he was brilliant at physics as well. He attracted the attention of a prof, and got accepted to grad school. He did quite well at the research area he entered in grad school.

Then there is John Moffat.

https://www.amazon.com/dp/0887626157/?tag=pfamazon01-20

John Moffat was my PhD supervisor's PhD supervisor. He was making his living as an artist in Paris. And in his spare time he was studying physics, in particular, general relativity and gravity. And he wrote a letter to Einstein. Which Einstein answered. And John started a correspondence, asking many questions and getting answers. Eventually, Einstein asked why John was asking him all these questions. Why was he not asking his professor? John explained that he had no university training at all, he was just a guy reading on his own. So Einstein got him into grad school at Cambridge.

 

[Vanadium 50]

It is not that a professor is unwilling to write me a letter.

I can only go by what you told us.

Is the person you RA'ed for willing to write you a letter?

No.

I think you need to expand beyond the Top 20. Do you have a reason why Caltech should take you over someone with a better pGRE, a stronger undergraduate background and better letters?

 

[PAllen]

Just as a point of info, the following claims the average pGRE of top 10 physics graduate programs is 902.

https://arxiv.org/pdf/1504.03952.pdf