Hermitik ve hermitik olmayan işlemciler

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 calculated. Science Code : 202.1.149 Key Words : PT symmetry, non-hermitic operators Page Number : 47 Supervisor : Assoc. Prof. Dr. Özlem YEŞİLTAŞ