Schrödinger’s Equation—¿after that session was I dead or alive or both?
My In2science placement took place between the 21st and the 25th of July at the London Centre for Nanotechnology, UCL. As the week began I was both nervous and excited. I was happy with the placement I’d been given—working alongside PhD students, experts in Physics, both theoretical and experimental. I could not have been placed anywhere better! On the first day, we had a tour of UCL and we were introduced to our Supervisors; Michael, Phil and Tom. They were very helpful and patient with us, myself and the two other students. By the second day we got into some hard-core experimental physics (or so it felt). Scanning-tunnelling microscopy is what we were introduced to by Toby, an experimental physicist who gave us in-depth explanations yet were very easy to understand (see photo below). This was fun, the aim was to scan the surface of graphite and with some luck try to see as close to the atoms as we could get. The tunnelling part comes from quantum physics and psi, the probability amplitude.
Although we didn’t get to see a perfect picture of the atoms, we got to be very hands on! As the week progressed we got to see various labs and experiments of physicists working with lasers, dust-free microscopes and liquid helium. We got talks on Quantum Physics Really Exists! and the creation (or not) of a quantum computer in the USA. We also learnt about the differences between Classical Physics and Quantum Physics. But for myself, leaning more towards theoretical physics, the week really got exciting when we began work on differential equations and Schrödinger’s Equation, by which I was feeling very excited yet somewhat intimidated by the complexity I thought such an equation would carry.
Time Independent Equation:
Time Dependent Equation:
Using calculus as a starting point we found and solved differential equations for exponential radioactive decay and more, leading to the point of using coding on the computer to create a interactive diagram of the quantum tunnelling process using Schrödinger’s Equation.
All in all I can say that it was a very productive and fascinating week which not only assured me of my passion for physics but opened my eyes to the wide array of possibilities a career in science could lead to.
By Maria B