Visual quantum mechanics

Description

Quantum mechanics is a difficult subject to explain as it relies on a lot of mathematics (Hilbert spaces, unitary operators, ...) not familiar from everyday experience. Techniques which visualise wave functions can thus be very useful to get more insight and intuition into the way in which the world works at the quantum mechanical level. This is especially true for complicated time-dependent phenomena, as they occur in e.g. quantum tunneling.

In this project you will study the mathematics necessary to solve for the quantum mechanical wave function in problems which go beyond those of simple textbook examples. You will then learn how to use modern techniques to visualise these wave functions using your own computer code.

Prerequisites

You need to take Quantum Mechanics III as a co-requisite, or must have taken it last year. You should not be afraid to do some Python or C++ programming and have a solid interest to spend time learning how to use modern visualisation tools (e.g. VTK).

Some background material

• Two somewhat older books by Bernd Thaller are useful starting points, as they come with pictures and movies (as well as the Mathematica notebooks to generate them); see the homepage of Visual Quantum Mechanics.
• An article "An open source virtual laboratory for the Schrödinger equation", by Figueras, Olivieri, Paredes and Michinel.
• Hydrogen wave function visualisation app by Daniel Svane.