Quantum mechanics is governed by the famous Schrödinger equation, which describes the time-evolution of a wave function of a quantum-mechanical system. Solving the time-dependent Schrödinger equation is in general hard (it being a PDE), so one often resorts to numerical techniques.
Standard finite-difference numerical methods work well provided one takes proper care of avoiding discretisation errors. With explicit access to wave functions and their time evolution, many aspects of quantum mechanics become much easier to explore and understand than is possible with only analytic tools.
In this project you will use concrete examples of quantum mechanical systems to study various numerical methods to solve and understand them.
Quantum Mechanics III or equivalent is required as a co-requisite. This is a very hands-on project in which you will run a lot of computer code, so you also need to have good Python skills or experience with another programming language, e.g. C++ or Julia.