**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.

A: Write Maxwell’s Equation.

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

B= B

_{0 }e^{i(k’.r-w’t) }(k’,B_{0 }are vectors btw),(here there is k’ and w’)

E=E

_{0}e^{i(k.r-wt)}(here there is k and w)

Prove k’=k and w’ = w.

B: Draw the 1D infinite well potential.

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

B: Now draw the 3

^{rd}eigenstate.

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.

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.

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.

C: A particle is thrown up in a resistive medium where F

_{res}depends on v.

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

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.

RESULT : Not Selected(Wait Listed).

- 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.