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...Show moreWe 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.Show less
The construction of the supersymmetric non-linear sigma model is presented. This model is then applied to the symmetry group SU(2N). The thesis considers the gauging of different subgroups of SU(2N...Show moreThe construction of the supersymmetric non-linear sigma model is presented. This model is then applied to the symmetry group SU(2N). The thesis considers the gauging of different subgroups of SU(2N), whereupon the particle spectrum of the theory is determined. The thesis concludes with an outline on how to proceed.Show less
