Self-adjoint Extensions of the Operators and Their Applications in Physics

ABSTRACT: In this thesis, self-adjoint extensions of some of the operators used in quantum mechanics are studied. First, the necessary mathematical background namely, the vector spaces and Hilbert space are reviewed. Secondly, the theorem of von-Neumann is introduced to determine the self-adjoint extension of the operators. The application of self-adjoint extensions of the momentum and spatial part of the Klein-Gordon equation is investigated. The concept of quantum singularity structure of the negative mass Schwarzchild spacetime is investigated by the wave obeying the Klein-Gordon equation. Keywords: Self-adjoint extensions, Hilbert-space, von-Neumann Theorem, Klein-Gordon equation. ……………………………………………………………………………………………………………………………………………………………………………………………………………………