Spektralteori for en-dimensionale tre-legeme kvantesystemer

Studenteropgave: Speciale (inkl. HD afgangsprojekt)

• Jonas Have
4. semester, Matematik, Kandidat (Kandidatuddannelse)
This thesis treats spectral theory for three-body quantum systems in one-dimension. Initially, a self-adjoint Schrödinger operator for a system with Dirac delta interactions is defined using a sesquilinear form. The exact domain of the Schrödinger operator is specified, and the essential spectrum is determined. To determine the essential spectrum a special case of the HVZ theorem is proven. Results regarding the resolvent of the Schrödinger operator is also proven.
In the final chapter, another case of the three-body quantum system is considered. In this case, perturbation theory is used to determine the existence of a discrete eigenvalue and the behavior of this eigenvalue as a function of the coupling constant $\kappa$. It is shown that for small values of $\kappa$ the behavior of the discrete eigenvalue is $\mathcal{O}(\kappa^4)$.
Sprog Engelsk 10 jun. 2016 76
ID: 234904993