Derivative and partial integral methods and Gauss integral's indefinite integral solution and its use in wave function in quantum mechanics and exact solutions of the wave function depending on position and time

Dila Başpınar; Ela BAŞPINAR; Nesrin BAŞPINAR; Umut Aldoğan

doi:10.70447/ktve.2239

Derivative and partial integral methods and Gauss integral's indefinite integral solution and its use in wave function in quantum mechanics and exact solutions of the wave function depending on position and time

Authors : Dila Başpınar, Ela BAŞPINAR, Nesrin BAŞPINAR, Umut Aldoğan

Pages : 55-63

Doi:10.70447/ktve.2239

View : 105 | Download : 1

Publication Date : 2023-10-30

Article Type : Research Paper

Abstract :[eng] This study, , solution of Gaussian Integral with differential equation [18,19]; By using the partial integral method, the indefinite integral solution by taking x under the differential [29,30,31] and the indefinite integral solution by taking the Gaussian integral under the differential [33,38,39] both harmonic series and function solutions are found. Indefinite integral solution of Gaussian Integral [38] In Quantum Physics, the wave function solution f(x,α) in terms of α variable in x position and k space by substituting it in wave function [44,45] and in one-dimensional time dependent Schrödinger equation, wave function equation [66, 67] is found. When the wave function in direct space is differentiated by by the partial integral method without using the approximate value of w(k)[50] in space k, the general wave equation in k space by position [74] and approximately the wave function f(x,α) [80] is found. min in space k depending on location and time the exact solution of the wave equations [83,89] and the Taylor Series solution give the wave equation [87,90] in k space according to position and time. [tur] Bu çalışma, , Gauss İntegrali’nin diferansiyel denklem ile çözümü[18,19]; kısmi integral yöntemi kullanılarak x diferansiyel altına alınarak belirsiz integral çözümü[29,30,31] ve Gauss İntegrali diferansiyel altına alınarak belirsiz integral çözümü[33,38,39] hem harmonic seri hem de fonksiyon çözümü bulunmuştur. Gauss İntegralinin belirsiz integral çözümü[38] Kuantum Fiziğinde dalga fonksiyonununda yerine koyarak x konum ve k uzayında değişkeni cinsinden dalga fonksiyonu çözümü[44,45] ve bir boyutlu zamana bağlı Schrödinger denkleminde, dalga fonksiyonu denklemi[66,67] bulunur.
Keywords : Quantum Algorithms and Quantum Circuits, Gaussian Integral, Derivative, Gauss İntegrali, Türev, Kısmi İntegral

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