Natanzon potansiyelleri üzerine On the natanzon potentials
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Dosyalar
Tarih
2007
Yazarlar
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Yayıncı
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
ÖZET Bu çalışmada, hipergeometrik fonksiyonların özellikleri kullanılarak, Schrödinger denkleminin çözümü olan dalga fonksiyonları, potansiyel fonksiyonu ve S- matrisinin belirttiği dönüşüm incelenmiştir. Birinci bölümde, hipergeometrik denklem ile ilgili bazı bilgiler verilmiştir. Potansiyel fonksiyonunun genel denklemi ve dalga fonksiyonunun hipergeometrik fonksiyona bağlı olan ifadesi elde edilmiştir. Genel potansiyel denklemindeki parametrelerin özel değerleri için özel potansiyellerin denklemleri belirlenmiştir. kinci bölümde, S-matrisinin belirttiği dönüşüm elde edilmiştir. Üçüncü bölümde, önce konfluent hipergeometrik Natanzon potansiyelleri verilmiştir, sonra dalga fonksiyonunun konfluent hipergeometrik fonksiyonuna bağlı olarak ifadesi incelenmiştir. Dördüncü bölümde, bu tezde çalışılan konu ile ilgili bir uygulama yapılmıştır. ANAHTAR KEL MELER: Schrödinger denklemi, Dalga fonksiyonu, Potansiyel, Hipergeometrik fonksiyon.
In this study, the wave functions which are the solutions of the Schrödinger equation, the potential function and the transformation which is determined by the S- matrix are investigated using properties of the hypergeometric functions. In the first chapter, pertinent background material about the hypergeometric equation is given. A general form of the potential function and expression of the wave function in terms of the hypergeometric functions are obtained. The equations of the special potentials are determined for the particular values of the parameters which are in the general potential equation. In the second chapter, the transformation which is determined by the S-matrix is obtained. In the third chapter, first confluent hypergeometric Natanzon potentials are given and then the expression of the wave function by confluent hypergeometric function is investigated. In the fourth chapter, an application is given for the subject which is studied in this thesis. KEY WORDS: Schrödinger equation, Wave function, Potential, Hypergeometric function.
In this study, the wave functions which are the solutions of the Schrödinger equation, the potential function and the transformation which is determined by the S- matrix are investigated using properties of the hypergeometric functions. In the first chapter, pertinent background material about the hypergeometric equation is given. A general form of the potential function and expression of the wave function in terms of the hypergeometric functions are obtained. The equations of the special potentials are determined for the particular values of the parameters which are in the general potential equation. In the second chapter, the transformation which is determined by the S-matrix is obtained. In the third chapter, first confluent hypergeometric Natanzon potentials are given and then the expression of the wave function by confluent hypergeometric function is investigated. In the fourth chapter, an application is given for the subject which is studied in this thesis. KEY WORDS: Schrödinger equation, Wave function, Potential, Hypergeometric function.
Açıklama
Anahtar Kelimeler
Matematik, Mathematics
