Regüler hahn dirac operatörü

The Dirac equation is regarded as a revolutionary milestone in the history of modern physics. As one of the foundational pillars of relativistic quantum mechanics, this equation not only provides a consistent explanation of the electron's spin-½ property but also predicts the existence of antiparticles, thereby opening a new era in theoretical physics. Furthermore, it has demonstrated remarkable success in accounting for the fine structure corrections observed in the hydrogen atom spectrum. In this thesis, we consider the Hahn–Dirac equation, which can be viewed as a generalization of the classical Dirac equation. The introductory section provides a comprehensive account of the historical development of the subject, accompanied by essential theoretical preliminaries that facilitate a deeper understanding of the topic. Additionally, fundamental mathematical concepts and results that will be utilized in subsequent chapters are systematically presented. The second and third chapters of the thesis offer a detailed examination of the Hahn–Dirac equation, focusing on its structural characteristics, mathematical properties, and physical interpretations. In the final chapter, the dissipative, accretive, and self-adjoint extensions of the Hahn–Dirac operator associated with the equation are investigated, and these extensions are expressed in terms of boundary conditions.