Interview tips for M.Sc. Physics application at Heidelberg University

Application to Heidelberg

After several wonderful undergraduate years at Leipzig, I applied to one of the best physics faculties on the planet and one of the most fairy-tale-like cities - Heidelberg. I had visited Heidelberg twice as a tourist and had fallen for the city.

Let’s break down how the admission procedure works according to Heidelberg’s website. There are two parts to the admission,

1. BSc grades (worth 15 points) (5th-semester grades if your final degree certificate is not available when you are applying)

2. Interview (worth 15 points)

The number of seats is for the program not limited. You are admitted to the program if you get $\geq 16$ points. If you have good grades in your BSc, you are almost there.

Now, jumping to the interview. You know beforehand the professors who will interview you; I highly recommend you google them before the date if you want. It’s just human nature to feel more comfortable talking to someone if you know something about them.

One of the most common questions I receive is, “How do I prepare for the interview?". The questions asked to summarize what you learned during your Bachelor’s.

Pointers for preparation

1. They would assume that you are well-versed in the following undergraduate subjects,
   • Classical mechanics (Including Lagrangian and Hamiltonian mechanics, aka Analytical mechanics)
   • Electrodynamics
   • Vibrations and Waves
   • Special relativity
   • Quantum mechanics
   • Statistical mechanics
2. If you know your gaps and loopholes, you can fill them conceptually by reading the chapters from David Tong’s lecture notes / Feynman’s lectures. Why the change of mind from Feynman to Tong? - In the past years, I have been reading Tong’s lecture notes as an attempt to concretize my foundations even more, and to date, I have read at least 5 of his notes, front to back, and honestly, they have so much more depth than Feynman’s lectures which was my previous recommendation for preparation - Which makes sense as Feynman’s lectures were given to first-year students approximately 60 years ago - Don’t get me wrong, I still occasionally reach out to Feynman lectures as they are always going to be an excellent resource if you need to brush up some of your concepts quickly. You can find all of them here. Remember, you are preparing for an interview; you do not have time to go front to the back of his notes, pick up a set of notes and go through the sections you don’t feel confident about.
3. A series of physics books by Daniel Fleisch is an excellent companion during this time. Most results and how they are derived in these books will be “obvious facts” that the professors might expect you to know. They are small booklets summarizing the main results of each of the following subjects.
   • A student’s guide to Maxwell equations (For Electrodynamics)
   • A student’s guide to Waves (For Vibrations and Waves)
   • A student’s guide to Schrodinger equation (For Quantum mechanics)
4. Apart from Tong and Feynman’s lectures - here are some goto resources one should keep in mind, particularly for Statistical Mechanics, Thermo, and Special relativity.
   • Thermal Physics by Blundell (Thermodynamics and Statistical mechanics)
   • Special relativity and Classical field theory by Leonard Susskind (The first three chapters should be good enough for Special relativity)
5. 🌟 If you have a friend who is very well versed in all these subjects, ask them to test your basic understanding of these subjects (Not someone who is looking to show off their knowledge, but rather someone who is genuinely willing to help - the first type of person will cause more harm than good)

As you will see, the theme of the questions can vary a lot. It is more about breadth than depth while you prepare.

Interview Questions

My most important advice is that keywords are much more powerful than an elaborate explanation during such an interview.

General questions

1. Why are you applying to Heidelberg?
   • There are 8-9 specializations at Heidelberg. Preferably talk about the one you are most interested in. Or, if there are a few faculty members you would like to work with, mention them. They want to see that you have a reason to apply, and both senses mentioned above should suffice.
2. What did you do for your BSc Thesis/ Project?
   • This is for people with a thesis, I am presuming during the BSc. The task here would be to summarize what you did as quickly as possible.

Physics questions

(Answer them as concisely as possible using the keywords, I’ll put the keywords in italics) - I am trying to recall exactly what I answered; I will write the answers exactly as I answered them.

1. How would you solve quantum mechanical Hydrogen atom?
   • Take the 3D Schrodinger equation, use separation of variables and then you will get a radial and an angular equation.
2. What would be the next step?
   • For the radial equation, we make a typical ansatz; for the angular equation, we have the spherical harmonics as the solution. (Yeah, I just said that we make a typical ansatz. If they had asked me what it exactly is, I would have said it. Answering quickly and pointing them in the right direction is better than taking time for a perfect answer. As I said, keywords can do magic).
3. What are the boundary conditions?
   • For the radial equation, the wavefunction should go to zero at the center. This ensures it doesn’t blow up for $r\to 0$. Also, it should go to zero at $r\to \infty $ because, for anything else, it physically doesn’t make sense. (Just like a finite charge, it makes sense for the electric field to be $\vec{E}=0$ for $r\to\infty$. If this is not the case, a finite charge will affect particles on the other end of the universe).
4. For such a system, why are the angular momentum quantities discrete?
   • It is due to the symmetry. We have the angles identified as $\theta\in(0,\pi)$ and $\phi\in(0,2\pi)$. This will give rise to the boundary conditions giving us discretized values for the angular momentum numbers for $l,m$.
5. How are the $l$ discretized?
   • Me : Umm, $l(l\pm1)$
     Interviewer : Seems like you don’t care about $\hbar$? (The question was asked with a cheerful tone)
     Me: Eh, it’s 1. (Cheeky smile audible in my voice)
     Interviewer : Haha, I guessed so. Good, let’s move on to a different topic.
6. How would you define temperature for any system?
   • Me : Uh, any system?
     Interviewer: Yeah, that is one of the physical quantities that can always be defined for any system.
     Me : (Sudden response while being worried) “Maxwell Boltzmann distribution” ?! (At the same time, the interviewer was hinting by saying think “mean energy”)
     Interviewer : Super.

     This probably is not a really complete answer. I should have asked do they mean a classical or a quantum system. Maxwell Boltzmann is one of the more classic solutions but definitely it is not applicable to any system . Maxwell Boltzmann distribution is the correct answer if the question was “How would you define the temperature for any system similar to a classical gas in equilibrium (A lot of classical scenarios - including something as crucial as the dark matter distribution or are idealized by this indeed and probably they just wanted to see if I know distrubtions and atleast the basic keywords in statmech - Hence the super I guess?.)

7. How would you define temperature in general?
   • It’s the vibrational energy of the molecules or the particles.

And that was it. I asked them how long it takes for the results to be out. They told me that it would be a couple of days.

Other questions I collected from the internet and colleagues.

• (Internet1) : What is the expected value of $x$ for an electron in vacuum? Ans. $\left<x\right> = 0$ from symmetry
• (Internet2): What are spherical harmonics?
• (Internet3): What happens to an electron excited in an atom, and what law is associated with it? Ans. It will decay using Fermi’s golden rule.
• (Alice1): Why do we not fall through the ground? (A question to begin with that was followed up further with how to solve the radial equation hydrogen atom and applying the boundary condition that the probability goes to 0 at the origin, so we can’t have electrons ‘falling’ into the nucleus)
• (Alice2): General particle physics questions: distinguishing fermions and bosons, summarising the particles of the standard model and their commonly known properties like the mass, charge, and spin (I don’t think they expected all properties of all the particles)
• (Bob1): Tell us about your bachelor thesis. If you didn’t have one, explain some projects that you did. They asked questions about those projects.
• (Bob2): Explain Maxwell’s equations
• (Charlie1): Explain the quantum mechanical interpretation of an atom (H atom)
• (Charlie2): Explain the quantum harmonic oscillator, probability densities in a 1D potential well, Schrödinger equation in 1D
• (Charlie3): Brief about Bachelor thesis, simple questions on the instrumentation, and general overview
• (Charlie4) : (I do not remember the exact questions as it was a long time ago, but the theme was quantum mechanics and why and how it’s an improvement over the Bohrs model)
• (Yara): Discussed two topics in detail: Hydrogen atom (QM) and Modes of heat transfer. Then we started talking about Cosmology. This part was more of a discussion session and not a Q&A.
• (Zack): Mostly questioned on gravitation, Kepler’s laws, etc.