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

dc.contributor.author	Emral, Kıymet
dc.date.accessioned	2013-08-14T06:48:37Z
dc.date.available	2013-08-14T06:48:37Z
dc.date.issued	2013
dc.identifier.citation	Emral, Kiymet. (2013). Self-adjoint Extensions of the Operators and Their Applications in Physics. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Physics, Famagusta: North Cyprus.	en_US
dc.identifier.uri	http://hdl.handle.net/11129/647
dc.description	Master of Science in Physics. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Physics, 2012. Supervisor: Prof. Dr. Özay Gürtuğ.	en_US
dc.description.abstract	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. …………………………………………………………………………………………………………………………………………………………………………………………………………………… ÖZ: Bu tezde, kuantum mekaniğinde kullanılan bazı operatörlerün kendi eşlenik uzantıları ele alınmıştır. İlk olarak, gerekli matematiksel altyapı olan, vektör uzayları ve Hilbert uzayı gözden geçirilmiştir. İkinci olarak ise, operatörlerin kendi eşlenik uzantılarını belirlemek için kullanılan von-Neumann teoremi tanıtılmıştır. Daha sonra uygulama olarak Momentum operatörü ve Klein-Gordon denkleminin uzaysal kısmının kendi eşlenik uzantıları incelenmiştir. Son olarak negatif kütle Schwarzschild uzay-zamanın kuantum tekillik yapısı Klein-Gordon denklemine uyan dalgalar için incelenmiştir. Anahtar Kelimeler: Kendi eşlenik uzantısı, Hilbert uzayı, von-Neumann Teoremi, Klein-Gordon denklemi.	en_US
dc.language.iso	en	en_US
dc.publisher	Eastern Mediterranean University (EMU)	en_US
dc.subject	Physics	en_US
dc.subject	Operator Theory - Selfadjoint Operators - Hilbert Space	en_US
dc.title	Self-adjoint Extensions of the Operators and Their Applications in Physics	en_US
dc.type	Thesis	en_US