Leiden University Student Repository

Wellens, Michael (2018)

Supersymmetry, or scaling difficult potentials easily

Bachelor thesis | Natuurkunde (BSc)

We first introduce the concept of partner potentials in non-relativistic quantum mechanics, i.e. a pair of potentials with the same spectrum, possibly except for a zero-energy ground state. We use this to define a family of partner potentials, giving us a technique to calculate the entire spectrum of a potential. The mechanism of partner potentials is then used for a quantum mechanical model of supersymmetry. It turns out that a special class of potentials exists where the spectrum can be determined very quickly using the techniques developed. We explore some of these potentials, called shape invariant potentials or SIPs and discover some simple properties of them. Finally, we take a quick look at a Hamiltonian with a $p^4$ term in it, discovering that for a small class of potentials, we can make a supersymmetric quantum mechanical model out of it.

supersymmetry

quantum mechanics

anti-commuting

partner potential

shape invariant potential

Author

Wellens, Michael

Faculty

Faculty of Science

Specialisation

Bachelor

Supervisors

Schalm, Koenraad

ECTS Credits

4

Language

en