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IMSc, Chennai -IPhD interview experience- Sayan Mondal | Physics After Engineering blog

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    So  let me share with you my Institute of Mathematical Science, Chennai interview experience. I didn’t have a particularly good interview, so I’m not expecting getting selected in this. There were 3 professors let’s call them A, B and C.
Prof A gave me a choice between Electrodynamics and Differential Equations.
I chose Electrodynamics.

A: Write Maxwell’s Equation.

I wrote them on the board.

A: now please remove the Maxwell correction term. And tell me if the equations are consistent.

Me: I tried to explain to them using the capacitor description that we were taught in Class 11-12. He listened to it and said to me that it is correct but asked me to show it through the four equations.
I was struggling, so Prof. C gave me some hint: take divergence on the equations and I did so. After struggling a bit, at last, I arrived to the conclusion that the charge flow is not being conserved, so we need Maxwell’s correction.   

Prof A now gives me the E and B components of an EM plane wave. He wrote them like this:

B= B0 ei(k’.r-w’t) (k’,B0 are vectors btw),(here there is k’ and w’)

E=E0ei(k.r-wt) (here there is k and w)

He asked me to

Prove k’=k and w’ = w.

I tried proving by putting them into the Maxwell equation but couldn’t finish, so they moved onto the next question.

Prof B now asked me about Quantum Mechanics.

B: Draw the 1D infinite well potential.

I did so.

B: write the Wavefunctions and energy values. (Energy Eigenstate and value)

I did so.

B: Now draw the 3rd eigenstate.

I did so.

B: Now imagine If the base wasn’t horizontal but slanting (like y=x), then how will the eigenstate change?

B: Give me the qualitative picture.

Me: Since k is dependent on E-V and this gets lower so K decreases and wavelength increase also the wavefunction amplitude is lower at higher V.

Then Prof C asked me if

The first Half cycle (the part between  x=0 and first node) of this modified V(x) have a bigger or smaller amplitude than the first half cycle of the normal particle in the box.

I struggled a bit, she gave a hint that it can be obtained by the property of wavefunctions.
I realized that

 The total Probability will be 1 and since the two other part has lower amplitude this will compensate and hence will be bigger, 

She agreed.

Then Prof C asks me a question on Classical Mechanics.

C: A particle is thrown up in a resistive medium where Fres depends on v.

I wrote the force equation.

C: What would be the velocity at time t->infinity.

ME: it will depend on the initial velocity.

C: Write the force equations in terms of v and solve the differential equation 

I did so and got an exponentially decaying function with a constant term.

Me: The velocity is constant at t->infinity as at some point the resistive force gets equal to mg and the ball has not acceleration so the ball is traveling in constant speed.

C: what is this velocity called?

Me: Critical Velocity? (I couldn’t recall the term)

C: No It is called Terminal Velocity.

                The interview ended here. The professors were super nice and gave hints at every point when I was struggling. IMSc is also a great institute.  Also, they provided free accommodation and Travel expenses. Food was really good and at a decent price.

RESULT : Not Selected(Wait Listed).

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Here are some other questions that were asked to other people :

  • Cycloid motion and Cyclotron motion of charged particle derivation. (This was not asked directly but the result arrived after successive questions on Lorentz force and diff equations)
  • A loop which is cutting a B field pulling a mass and when there is flux changing the block is moving down until the flux in a loop starts changing again. Leading to a Periodic motion. something of that sorts. So, the questions were quite doable.
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