Hermitian and non-hermitian operators


Thesis Type: Postgraduate

Institution Of The Thesis: Gazi Üniversitesi, Fen Bilimleri Enstitüsü, Turkey

Approval Date: 2013

Thesis Language: English

Student: NAFİYE KAPLAN

Supervisor: ÖZLEM YEŞİLTAŞ

Abstract:

In this thesis discrete symmetries in quantum mechanics, PT symmetry and non Pseudo-Hermitian Hamiltonians, which have recently attracted a lot of interest are examined. By evaluating PT symmetric non Hermitian Hamiltonian model which is known as a Hamiltonian Swanson model in the literature, metric operator which provides to obtain Hermitian equivalent Hamiltonian is obtained. As an example of these general quantum systems, the most general Hamiltonian was also given by differential operators, a transformation of a Sturm-Liouville processor was evaluated. In addition, in this thesis, quantum Brachistochrone problem was evaluated in the frame of complex quantum mechanics and the spectrum is obtained for PT symmetric matrix Hamiltonian. On the other hand, C operators is obtained using a necessary algebra. For the Brachistochrone problem, the shortest evolutione time is T calculated.