Project ideas

Below are a list of project ideas, no matter who you are, you may attempt any of these. You should assume that this list is up-to date. They are roughly ordered in complexity from easiest to hardest. If you would like to ‘claim’ one of these projects or add projects let Joseph Tooby-Smith know, or make a pull-request to the PhysLean website repo.

The reflectionless potiential in quantum mechanics

Available

Formalize the properties of the reflectionless potential in quantum mechanics, following the formalization of the quantum harmonic oscillator.

Tight-binding model for graphene

Available

PhysLean already contains the tight-binding model for a chain. This project would aim to genearlize that to do the tight-binding model for graphene. A reference can be found here.

Definition of the bosonic and fermionic Hilbert spaces

Available

Define the Hilbert space of a single bosonic and a single fermionic particle. These can be found in these note. Part of this will involve defining the Lorentz-invariant measure and the mass-shell manifold.

Quantum particle on a ring

Available

Formalize the quantum mechanics of a particle on a ring, see e.g. the wikipedia page. See also, this Zulip discussion.

The two Higgs doublet model potential

Available

The aim of this project would be to prove Theorem 1, 2 & 4 of this arXiv(hep-ph):0605184. This is related to the two Higgs doublet model, which corresponds to a model of the universe with a proposed extra Higgs doublet.

Properties of grand unified theory groups

Available

Prove the group theoretic properties of the grand-unified theories: SU(5), Spin(1) and Pati-Salam, as they appear in this note. Some of these results appear on the todo list.