Around 110 students were shortlisted for the interview round of department of Physical Sciences at IISER Kolkata, based on the all-India ranks of the candidates in JAM and JEST exams for a total of 5 seats in their Integrated PhD program. In addition to that, every candidate had to send two letters of recommendation to the department. My interview was conducted on 29th June. There were five professors in my panel. They first asked me my favourite topics to which I replied, ‘Quantum Mechanics’ and ‘Lagrangian and Hamiltonian Mechanics’. They directly started asking the questions. Following questions were asked by the panel.
1-i) Plot sin(x^2).
1-ii) What will be the asymptotic behaviour of the nodal distance i.e. the distance between two consecutive nodes?
2-i) Write the Lagrangian of a charged particle in an EM field.
2-ii) Apply a Gauge transformation and re-write the Lagrangian.
2-iii) Are the equations of motion obtained from Lagrangian invariant under a gauge transformation?
2-iv) Can you give an example of a point transformation for a harmonic oscillator potential? Show that the action principle is invariant under such a transformation.
Prof-3: Topic: SHM
3-i) Plot the time period of a simple pendulum vs. distance from the center of the Earth. The answers will be dependent upon whether we are inside Earth or at a distance h from its surface. Both the cases were to be shown in the plot.
Prof-4: Topic: Quantum Mechanics
4-i) Write down the time-independent Schrodinger equation (TISE) for a constant force.
4-ii) What will be its solutions? (Airy functions)
4-iii) Now, instead solve TISE in the momentum space. Is the solution normalizable? How will you normalize it? (I used Dirac-orthonormality trick)
Prof-5: Topic: Hydrogen atom
5-i) The prof gave a wave function for an electron in the hydrogen atom as a linear superposition of three distinct eigenfunctions. When you take a measurement, what will be the different energies obtained and with what probabilities? What will be the different values of L^2 (angular momentum squared) obtained and with what probabilities?
5-ii) Two eigenfunctions in the wave-function had same value of the principle quantum number (n) i.e. 2. Now, if the wave-function collapses to a state where n=2, what will be the new energies obtained and with what probabilities? What will be the new values of L^2 (angular momentum squared) obtained and with what probabilities?
With this question, my interview concluded. It lasted for around 50 minutes. This interview was a wonderful experience. The interviewers were very friendly and helpful at every step.
My Opinion: Based on these questions, I feel that it was necessary that a candidate has solved a lot of problems. A thorough practice of the questions given in Quantum Mechanics by Griffiths and Classical Mechanics by Goldstein will help crack the interview questions in these two topics.
I was initially wait-listed.
Update (10/08/2020); I got selected in the program.