International Astronomy and Astrophysics Research Journal https://journaliaarj.com/index.php/IAARJ <p style="text-align: justify;"><strong>International Astronomy and Astrophysics Research Journal</strong>&nbsp;aims to publish high-quality papers (<a href="http://www.journaliaarj.com/index.php/IAARJ/general-guideline-for-authors">Click here for Types of paper</a>) in all areas of Astronomy and Astrophysics. The journal also encourages the submission of useful reports of negative results. This is a quality controlled, OPEN peer-reviewed, open access INTERNATIONAL journal.</p> <p style="text-align: justify;">Every volume of this journal will consist of 4 issues. Every issue will consist of minimum 5 papers. Each issue will be running issue and all officially accepted manuscripts will be immediately published online. State-of-the-art running issue concept gives authors the benefit of 'Zero Waiting Time' for the officially accepted manuscripts to be published. This journal is an international journal and scope is not confined by the boundary of any country or region.</p> en-US International Astronomy and Astrophysics Research Journal Generalization of Quantum Mechanical Wave Equation in Spherical Coordinate Using Great Metric Tensors and a Variable Gravitational Scalar Potential https://journaliaarj.com/index.php/IAARJ/article/view/22 <p>In this research work, the Riemannian Laplacian operator for a spherical system which varies&nbsp; with time, radial distance and time was obtained using the great metric tensors and a varying gravitational scalar potential. Furthermore the obtained Laplacian operator was used to obtain the generalized quantum mechanical wave equation for particles within this field. The Laplacian operator obtained in this work reduces to the well known Laplacian operator in the &nbsp;&nbsp;&nbsp;limit of <img src="/public/site/images/sciencedomain/Capture_11.PNG">, and it contained post Euclid or pure Riemannian correction terms of all orders of&nbsp;<img src="/public/site/images/sciencedomain/Capture_2.PNG"> . Also the generalized quantum mechanical wave equation obtained, in the limit of&nbsp;<img src="/public/site/images/sciencedomain/Capture_12.PNG">reduces to the well known Schrodinger mechanical wave equation, and in the limit of <img src="/public/site/images/sciencedomain/Capture_21.PNG">contained additional correction terms not found in the well known Schrodinger wave equation. Hence the results in this work satisfy the Principle of Equivalence in Physics.</p> A. U. Maisalatee W. L. Lumbi I. I. Ewa M. Mohammed Y. K. Kaika ##submission.copyrightStatement## 2020-07-30 2020-07-30 1 9