Özel bir radyal schrödinger dekleminin uygun simetriler yardımı ile çözümü
Yükleniyor...
Dosyalar
Tarih
2016
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Trakya Üniversitesi Fen Bilimleri Enstitüsü
Erişim Hakkı
info:eu-repo/semantics/restrictedAccess
Özet
Bu çalışmada; 2.,3. ve 4. bölümlerde adi diferansiyel denklemler, nokta dönüşümleri, sonsuz küçük dönüşümler, üreteç ve üreteçlerin normal formları, adi diferansiyel denklemlerin Lie nokta simetrileri ve simetri koşulları hakkında kısa bilgiler verilmiş, simetrileri bilinen bazı adi diferansiyel denklemlerin çözümleri gözden geçirilerek bir veya iki simetrisi bilinen bir veya ikinci mertebeden adi diferansiyel denklemlerin çözüm yöntemlerinden bahsedilmiştir. Çalışmanın 5.3. bölümde V(r) ? 0 potansiyeline sahip bir radyal Schrödinger denklemi ikinci mertebeden özel bir denkleme dönüştürülmüş, bu denklemin uygun simetrileri ile bulunan çözümleri denklemin klasik çözümü ile karşılaştırılmıştır.
abstract
In this study, it is given short knowledge about ordinary differential equations, point transformation, infinitesimal transformations, generator and normal form of generators, Lie point symmetries of ordinary differential equations and symmetry conditions in chapter 2,3 and 4. By considering the solutions of some ordinary differential equations which are known their symmetries it is mentioned about the methods of solutions of first or second order ordinary differential equations which are known one or two symmetries. In the subsection 5.3 of the study, a radial Schrödinger equation which has got the potential V(r) ? 0 is transformed into a special equation. The solutions which are found by using appropriate symmetries of this equation are compared with the classical solution of the equation.
abstract
In this study, it is given short knowledge about ordinary differential equations, point transformation, infinitesimal transformations, generator and normal form of generators, Lie point symmetries of ordinary differential equations and symmetry conditions in chapter 2,3 and 4. By considering the solutions of some ordinary differential equations which are known their symmetries it is mentioned about the methods of solutions of first or second order ordinary differential equations which are known one or two symmetries. In the subsection 5.3 of the study, a radial Schrödinger equation which has got the potential V(r) ? 0 is transformed into a special equation. The solutions which are found by using appropriate symmetries of this equation are compared with the classical solution of the equation.
Açıklama
Anahtar Kelimeler
Simetri, Radyal Schrödinger Denklemi, Üreteç, Symmetry, Radial Schrödinger Equation, Generator
