Genelleştirilmiş koherent haller ve matematiksel fizikte uygulamaları
Küçük Resim Yok
Tarih
1999
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Ege Üniversitesi
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
ÖZET GENELLEŞTİRİLMİŞ KOHERENT HALLER VE MATEMATİKSEL FİZİKTE UYGULAMALARI Özeren, Serhat F. Doktora Tezi, Fizik Bölümü Tez Yöneticisi: Prof. Dr. Fevzi Büyükkılıç Ocak 1999, 67 sayfa Bu tezde, koherent haller metodu ele alınarak, kuantum mekaniksel problemlerin çözümü üzerinde çalışılmıştır. Bu maksatla öncelikle, standart koherent haller Glauber' in tanımına göre incelenmekte ve daha sonra Perelomov tanımı kullanılarak Lie gruplarına genelleştirilmektedir. Özel olarak, kütlesi zamana bağlı bir osilatör problemi ele alınarak, kuantum sisteminin Hamiltoniyeni SU(1,1) Lie cebrinin operatörleri cinsinden yazılmış ve böylece SU(1,1) Lie grubunun koherent halleri yardımıyla ilgili problemin hareket denklemleri elde edilmiştir. Son olarak, koherent hallerin minimum belirsizliğe sahip olmasının kuantum mekaniksel problemlerin çözümüne getirdiği kolaylıklardan yararlanılarak, genelleştirilmiş istatistiksel termodinamik çerçevesinde Landau diamagnetizması incelenmiş ve sonuçlar tartışılmıştır. Anahtar sözcükler: Koherent Haller, Lie grubu, diamagnetizma
VI ABSTRACT GENERALIZED COHERENT STATES AND APPLICATIONS IN MATHEMATICAL PHYSICS Özeren, Serhat F. Ph.D. in Physics Supervisor: Prof. Dr. Fevzi Büyükkılıç January 1999, 67 pages In this work, considering the coherent states (CS) method, the solutions of some quantum mechanical problems have been studied. For this purpose, firstly, standard CS have been investigated by means of Glauber definition then they are generalized to Lie groups using Perelomov definition. Specifically, considering a problem of an oscillator where the mass is time dependent, its Hamiltonian has been written down in terms of SU(1,1) Lie algebra and the equations of motion of the related problem have been obtained by the help of the CS of SU(1,1) Lie groups. Finally, making use of the ease which comes to the solutions of the quantum mechanical problems from the fact that CS have minimum uncertainty, in the frame of generalized statistical thermodynamics, Landau diamagnetism has been investigated and its results have been discussed. Keywords: Coherent states, Lie groups, diamagnetism
VI ABSTRACT GENERALIZED COHERENT STATES AND APPLICATIONS IN MATHEMATICAL PHYSICS Özeren, Serhat F. Ph.D. in Physics Supervisor: Prof. Dr. Fevzi Büyükkılıç January 1999, 67 pages In this work, considering the coherent states (CS) method, the solutions of some quantum mechanical problems have been studied. For this purpose, firstly, standard CS have been investigated by means of Glauber definition then they are generalized to Lie groups using Perelomov definition. Specifically, considering a problem of an oscillator where the mass is time dependent, its Hamiltonian has been written down in terms of SU(1,1) Lie algebra and the equations of motion of the related problem have been obtained by the help of the CS of SU(1,1) Lie groups. Finally, making use of the ease which comes to the solutions of the quantum mechanical problems from the fact that CS have minimum uncertainty, in the frame of generalized statistical thermodynamics, Landau diamagnetism has been investigated and its results have been discussed. Keywords: Coherent states, Lie groups, diamagnetism
Açıklama
Anahtar Kelimeler
Fizik ve Fizik Mühendisliği, Physics and Physics Engineering, Koherent yapılar, Coherent structures, Lie grupları, Lie groups
