This is what a theoretical physics exam looks like at university
Hey everyone, today i’m going to show you inside a physics exam. I know that some of you might be interested to know exactly what studying physics is like and therefore what sort of exams and assessment looks like. So I have here a theoretical physics exam and I will say as a disclaimer, the questions in here I have edited so that they’re not exactly the same as an exam I took although it is based on a real exam. I’ve done this for two reasons; one, so that my uni doesn’t arrest me for publishing a real exam and two, is so that I can give you guys some solutions as well that are sort of fully worked and available elsewhere online in like textbook solutions. Having said that it does cover the same ideas that you would expect and that I definitely saw when I took an exam like this for the first time. Now the exam i’ve replicated is a theoretical physics exam from a third-year university course and it would take you three hours to do this exam and there are four questions so let me show you what it looks like. So this exam is going to cover most areas of theoretical physics, that’s a bit of classical mechanics, some quantum mechanics and special relativity. So let’s have a look. First up we’re going to have a classical mechanics problem and this is one that deals with a lagrangian. So we’ve actually got a double pendulum here and this is probably a bit of a typical problem. So you’re given a double pendulum and you’re asked first of all to find the lagrangian. So that’s essentially a way of finding out how to describe the system when the system is quite complicated. Then you want to find the equations of motion, that’s probably where you’re going to get a lot of marks as well because they might be a bit complicated and there’ll be a lot of calculus involved. Then you’re asked to describe the properties of a chaotic system. That’ll be saying something like a chaotic system, which a double pendulum is, well small deviations in where it starts or in the initial condition can lead to vastly different outcomes over time. And then lastly for this question we’ve got, explain the significance of Noether’s theorem. Moving on to part two, now we have a quantum mechanics problem. So this is actually from Griffiths, a really good quantum mechanics textbook and it’s about time independent perturbation theory. Now often when you work with quantum mechanics problems you’re dealing with say, a particle in a Infinite square well but perturbation theory deals with if there is a sort of blip or a bump. A perturbation in that square well so it’s no longer just a perfect square. Have a look in the description and I will link the solution here of how to do this. Our third question is also a quantum mechanics problem, it’s dealing with some sort of identities, commutator relations and really it’s a whole bunch of proofs. When I was doing sort of this exam, getting to this page, the page of quantum mechanics proofs, and to show things, is where my heart sinks because those are to me the hardest questions. Using mathematical induction or otherwise show that this is true. The classic ‘or otherwise’ statement, means really do it using the way they mentioned at the start otherwise you’ve got some crazy idea up your sleeve, I don’t know. Maybe if you’re clever you can think of another way to do it but usually when they give you a hint like this it’s a good idea to go with the hint. Part C I would probably find pretty tricky in this exam and it’s showing a relation that’s got something to do with Ehrenfest theorem. I don’t know how to pronounce that, I barely remember that theorem but I know, this has got something to do with it. Then part D we’re finishing off with a question about spin. The spin question really comes down to using linear algebra and it’s a useful application of some of the maths you learn quite early on. So finding a normalization constant and expectation values. Lastly, we have one whole question about special relativity. What makes special relativity difficult in say third-year is not the idea of sort of time dilation, and length contraction but it’s moving into using tensors and describing things in four-space. So that’s you can see this little notation here with the greek letters. That’s called a four-vector and it can be pretty tricky and be an obstacle to actually describing sort of space-time and special relativity. So because of that and because you would have just learned how to use these four-vectors, most of these questions here are just sort of kind of manipulation of four-vectors and once you really master these I think you might be able to go on to being good at things like general relativity and really getting into deeper into theoretical physics concepts. That isn’t the road I went down, but I think they were still pretty cool to learn about. I hope no one gets too stressed out looking at this exam that i’ve showed you because whilst this is pretty realistic of what you can expect, if you haven’t taken the course and subjects that are relevant to what i’m showing you, it can probably look overwhelming. Even me looking back on this now i’m like, geez how did I do any of this? I can’t remember some of this stuff now. But when you’re in that mindset of learning and studying for a course then it’s not so alien to you, then something like this would feel possible if you’re actually immersed in that environment and you’ve done the work leading up to it. Thanks for watching and if you have any questions about this exam or what others might look, like please let me know.