SU(3) grubunun homojen uzayında diferansiyel operatörler
Küçük Resim Yok
Tarih
2021
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Trakya Üniversitesi
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
Bu tez çalışmasının birinci bölümünde grup, homojen uzay, metrik matris ve diferansiyel operatörler hakkında temel bilgiler verildi. İkinci bölümde SU(3) grubunun homojen uzayının parametrik bir ifadesine göre metrik matris ve Laplace-Beltrami operatörü ifade edildi. Daha sonra bu operatörle oluşturulan özdeğer-özfonksiyon probleminin çözümü verildi. Çözümde ortaya çıkan fiziksel sistemin dalga fonksiyonu elde edildi ve sistemin potansiyeli ile dalga fonksiyonunun grafikleri verildi. Daha sonra SU(3) grubunun diğer diferansiyel operatörleri olan I^2 ,I_3 ,Y operatörleri ifade edildi. Benzer şekilde bu operatörlerle oluşturulan özdeğer-özfonksiyon problemlerinin çözümleri verildi.
In the first part of this thesis, the basic information about group, homogeneous space, metric matrix and differential operators was given. In the second chapter, the metric matrix and Laplace-Beltrami operator is expressed according to a parametric expression of the homogeneous space of the group SU(3). Then, the solution of the eigenvalue-eigenfunction problem obtained by the operator was given. The wave function of the physical system derived from the solution were obtained and, the potential function and the wave function of the system were drawn. Then, the other differential operators of the SU(3) group such as I^2 ,I_3 ,Y operators were expressed. Similarly the solutions of the eigenvalue-eigenfunction problems induced by these operators were given.
In the first part of this thesis, the basic information about group, homogeneous space, metric matrix and differential operators was given. In the second chapter, the metric matrix and Laplace-Beltrami operator is expressed according to a parametric expression of the homogeneous space of the group SU(3). Then, the solution of the eigenvalue-eigenfunction problem obtained by the operator was given. The wave function of the physical system derived from the solution were obtained and, the potential function and the wave function of the system were drawn. Then, the other differential operators of the SU(3) group such as I^2 ,I_3 ,Y operators were expressed. Similarly the solutions of the eigenvalue-eigenfunction problems induced by these operators were given.
Açıklama
Yüksek Lisans
Anahtar Kelimeler
Matematik, Mathematics
