appeared for the I-PhD interview at IMSc, Chennai in 2018 and got selected in the same. I had qualified for the interview through CSIR-NET exam with a rank of 122.
About the interview:
I was questioned in quantum mechanics, electrodynamics and mathematical physics(out of these 3 only mathematical physics was the subject proposed by me when they asked for another subject I can answer after the first 2 were done; the first two subjects they didn’t give me an explicit choice on- I knew the answers to the quantum and electro questions they asked so I just went with it- I explained in relatively more detail so I guess that took all the allotted time for these subjects anyway).
First part of the interview is the panel members going over your educational background and your activity in any gap there might be since your last degree. They did this for me as well. In this part of the interview, I had it a little easier as I had attended a summer school at IMSc in 2014, which was evidence that I had been interested in coming into a physics research career for a long time by then, and supported my statement that I could actively make the shift in my career only recently due to personal circumstances. In fact I had even met one of the panel members(who had taught in that summer School) around 1.5 years earlier for career advice, and he even recognized me.
First question was solving the harmonic oscillator problem using ladder operator method. I was able to derive the solution from scratch, and the panel, for most part of the interview, was patient when I needed a few more moments to pause and think. This was lucky for me as I was thorough with the harmonic oscillator derivation from studying it in Griffiths book, and could explain every step in good continuity, including for example the point that the ladder operators were guessed with inspiration from trying to factorize the Hamiltonian, etc. This derivation itself took a while, with the panelists asking questions now and then to make sure I actually understood every single thing that was going on in the steps- sorry but i cant recall all the little questions in detail as I’m writing this a year since the interview. After this derivation, there were 1 or 2 follow up questions where they gave new Hamiltonians to solve(again sorry but I don’t remember the exact hamiltonian). Although at first it looked tough, it could be noticed that the new Hamiltonian commutes with the Hamiltonian of the harmonic oscillator, hence it has the same set of eigen states, and now since the wave function from solution is same, we could substitute the energy eigen value equation of of the old Hamiltonian into the corresponding equation for new Hamiltonian hence getting the energy levels of new Hamiltonian. I think one of the new Hamiltonians they had given was H^2 (if I am not mistaken), where H is hamiltonian of harmonic oscillator. I understand this last question was probably vague the way I explained, but I hope you got a taste of on-the-spot thinking they expect.
Electromagnetic theory questions:
Next question was on method of images, where they asked to solve for potential, given a metallic sphere and at first 1 charge outside, then 2 charges outside on the same axis. To this question I started my answer from the mathematics behind the method of images, that is how the method is based on Poisson’s equation and the uniqueness theorem. And I solved by framing the relevant equations.
Mathematical Physics questions (by choice) :
Then I was given a choice on my next subject, to which I replied mathematical physics. They then asked me to solve a bunch of integrals, one by one. I needed a clue to solve many of them though. but i could solve most of the unknown ones when given that one hint in the first step. The methods typically involved complex integration, partial fraction, and also in of one case there was some manipulation involving differentiation/integration of an integrand whose answer is known and substituting that known answer etc- again sorry but I forgot the exact integrals asked. Overall I would say my performance in mathematical physics was not too good, as I needed hint in most questions, although they didn’t give that much time to think in this part of the interview and they seemed to be less patient if I took some ‘thinking time’.
All in all it looked like preparation for such an interview should be sufficient if you can work out problems in Griffiths books of quantum mechanics and electrodynamics, with full understanding of the theory. They do seem to ask from the more basic parts of syllabus for I-PhD level and seem to be more interested in the cleanness(basing every step on sound logic and accepting that you don’t know something when that is the case) of your approach, and perhaps your ability to handle a problem that they know will be just outside your comfort zone. Honestly, I feel you shouldn’t worry much about ‘just missing the chance’ in the interview, as I feel these interviewers (in IMSc atleast) seem to be considerate if you are not from physics background, are ready to give hints when you may get stuck, are overall good judges of your potential in physics research and won’t simply throw you away for a few silly mistakes etc. Also, not to discourage you, but after all we b.tech people are sacrificing significant financial comfort to do physics research in India, so we must make use of feedback from the panelists to gauge our own potential in this field, especially since some areas like string theory (high energy theory in general) are very abstract math intensive and highly competitive due to less number of post doc seats compared to the number of applicants, though it looks interesting when we read popular articles.
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