Interview Experiences

I had my IMSc interview on the 17th of May 2022 from 6 pm to 7 pm. It was an online interview. In my panel there were two professors, one was Sayantan Sharma and another was Sanatan Digal. Let's assume one is Prof A and another is Prof B

After joining the interview, Prof A introduced himself and told me that he was the person who sent me the mail regarding the interview. He also mentioned that at IMSc no experimental research is done, only theory and sometimes taking data from experiments some theoretical prediction is done here. He asked me if I knew about their integrated PhD program. I replied, "Yes, I have gone through the website". After that, they proceeded to the interview.

Prof A: write down the Lagrangian for Simple Pendulum.

Me: I wrote it correctly

Prof A: derive the equation of motion of a simple pendulum from the Lagrangian without small-angle approximation (Differential Equation).

Me: Derived it correctly

Prof A: Solve the differential equation

Me: It is basically a highly non-linear equation with a "Sine" term, especially known as the "Sine-Gordon" equation. It cannot be solved analytically and the integral equation that we can derive can be solved using 'Elliptic Integral' and the solution is known as 'Soliton Solution' But I did not know all of these. The only thing that I know was that it cannot be solved analytically. So, when he asked me to solve it, I was surprised. I asked repeatedly," Should I need to solve it without approximating sine term". I know how to solve it after taking 2 to 3 terms (Anharmonic oscillator problem). 

I think the prof understood that it can't be solved by me so he goes to the next part

Prof A: Find out the unstable equilibrium point

Me: From the potential, I found the unstable points

Prof A: If I give a potential equal to '2mgl', how much time does it take to reach the unstable point?

Me: At first, I said that I need to solve it, then Prof gave me a hint, the 'Unstable point', I said it will take ' Infinite amount of time to reach' 

Prof A: Very Good, :D

Prof A: Write down the 'Hamiltonian for this system'

Me: I wrote it down

Prof A: What is the conventional form to write the Hamiltonian?

Me: It should be a function of momentum and position, I changed it accordingly. At first, it was a function of velocity

Prof A: Let's assume the bob of the pendulum as a quantum particle and write down the Schrodinger equation. 

Me: Wrote it down

Prof A: Change the momentum in classical Hamiltonian as momentum operator in quantum mechanics

Me: I changed it.

Prof A: Use small-angle approximation and derive the Schrodinger equation from it

Me: I wrote it down

Prof A: So, you derived it from classical mechanics, in which condition does a classical harmonic oscillator behave as a quantum harmonic oscillator?

Me: In the case of a small angle.

Prof A: Okay, thank you

After that Prof B proceeded

Prof B: Hello Sidhartha, Write down Lorentz force equation

Me: Wrote it

Prof B: If the charge is moving in the magnetic field where its velocity vector is not perpendicular to the magnetic field what will the motion looks like

Me: Sir it would be a helical path

Prof B: Okay, Now assumes a charged particle is moving with a constant velocity along X-axis, there is an electric field along X-axis and a Magnetic field along Y-axis. What will be the trajectory of the particle in this case?

Me: I told him; it would be a Cycloid motion along X-axis

Prof B: Explain it

Me: As the particle is moving the magnetic force is along Z-axis and the electric force is along X-axis. So, the resultant is along the X+Y direction. As the speed increases, the magnetic force is also increasing but there is also an electric force it will resist the charged particle from bending along Z-axis. So, it will move along X-axis.

Prof B: Are you sure that the motion will not be along Z-axis?

Me: Sir it will be along Z-axis

Prof B: Why are you changing direction 90 degrees? stick to your answer and explain it.

We both are laughing at this time when I'm trying to change my answer

Me: okay sir. Then it will be an unbounded motion along the X-axis.

Prof B: When will the velocity of the particle be '0'?

Me: when it is on the X-axis

Prof B: Okay, thank you

He wanted me to explain why it is '0' on X-axis, but as the time was over, he told me to think about it later.

I am not sure about my second answer. He told me to do all the things without any mathematics

After that, they took a picture of me with my i-card and told me to leave the meeting.

The interview was 70 minutes long and I enjoyed it very much.

One of the professor give me a potential in central force motion and asked me to solve for its equation of motion from the graph of the potential. Another gave me a linear homogeneous differential equation. Last question was from quantum mechanics.