A master thesis from Aalborg University
Spectral Theory for One-Dimensional Three-Body Quantum Systems
[Spektralteori for en-dimensionale tre-legeme kvantesystemer]
Author(s)
Term
4. term
Education
Publication year
2016
Submitted on
2016-06-07
Pages
76 pages
Abstract
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 $\mathcal{O}(\kappa^4)$.
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