Study of Schrödinger Particles under the Influence of a Kratzer Molecular Potential in a Global Monopole Spacetime Background Plus a Wu-Yang Magnetic Monopole

Abstract

Global monopoles are topological defects predicted by the Grand Unified Theory throughout the transition phase of the primordial universe. They are formed as a byproduct of spontaneous global symmetry breaking. Their behavior resembles that of the elementary particles with their energies concentrated close to the core of the monopole. They do not have gravitational interactions but they are known to modify spacetime geometry. It is an interesting topic to study Schrödinger particles in a Kratzer Molecular potential in the Global Monopole Spacetime background and under the influence of a Wu-Yang Magnetic Monopole. Some modifications in the spectroscopic structure of such molecular interactions have been observed and reported. This study presents the use of the Schrödinger equation to precisely describe the motion of a particle in the presence of Kratzer potential and a Wu-Yang magnetic monopole. The radial equation was derived and solved to yield the eigenfunctions and eigenvalues for the problem. Keywords: PDM Shrödinger Equation, Point-like Global Monopole, Topological Defect, Kartzer Potential, Wu-Yang Magnetic Monopole.

Global monopoller, Büyük Birlesik Teori tarafindan erken evrenin geçis fazinda öngörülen topolojik kusurlardir. Bu topolojik kusurlar, spontan global simetri kilmasinin bir sonucu olarak ortaya ikarlar. Davranslari elementer parçaciklarinkine benzer; enerjileri monopolün gekirdegine yakin yogunlasir. Gravitasyonel etkilesim göstermese de. uzay-zaman geometrisini degistirdikleri bilinir. Global Monopole uzay-zaman arka planinda ve Wu-Yang Manyetik Monopolden etkilenen Kratzer moleküler potansiyel içinde Schrödinger parçaciklarnin incelenmesi ilging bir konudur Bu moleküler etkilesimlerin spektroskopik yapisinda bazi ayarlamalar gözlemlenmis ve belgelenmistir. Bu çalisma, Global Monopole uzay-zamaninda, Kratzer potansiyeli ve Wu-Yang manyetik monopolden etkilenen kosullarda, göreli olmayan bir kuantum parçaciginin hareketini kesin olarak tanimlamak için Schrödinger denklemini kullanir. Karsilk ge-len radyal denklem, problemin özfonksiyonlarn ve özdegerlerini belirlemek için türetilmis ve çözülmüstür. Anahtar Kelimeler: PDM Shrödinger Denklemi, Nokta Benzeri Küresel Tek Kutup, Topolojik Kusur, Kratzer Moleküles Potansiyel, Wu-Yang Manyetik Tek Kutup.