A mathematical modeling concept of the time dependent Schrödinger's equation using Maxwell's equations and special relativity.
Abstract
This theoretical study aims to derive the time dependent Schrödinger's equation using the electric field wave equation derived from Maxwell's equations and Einstein's relativistic energy-momentum relation. First, the electric field wave equation is derived from Maxwell's equation. Where the solution of the wave equation is a function of the frequency and wave function, and in order to associate the solution of the wave equation with the properties of particles, the frequency is expressed in terms of photon energy and the wave function is expressed in terms of photon momentum and it was done using special relativity, and then it became clear that it is possible to express energy and momentum of the photon with partial differential forms called operators. . By symmetry, it is very reasonable to assume that a particle can have the wave-particle duality. Therefore, last, it was established a wave equation for a moving particle by replacing the vector of the electric field with the wave function where the two terms are related to the numerical density of the photon, and the expression of energy and momentum of particle with their operators.
References
-Hand A. F. J. Levi, 2006. Applied Quantum Mechanics. Second Edition. Cambridge University Press.pp 57-79.
-Daniel Fleisch,2008. A Student’s Guide to Maxwell’s Equations. Cambridge University Press.pp 112-124.
- Georgios Tsaparlis, .2001.Towards A meaningful Introduction to the Schrodinger Equation through Historical and Heuristic Approaches .Research and practice in Europe. Vol. 2, No. 3, pp. 203-213
-Mohammed Ismail Adam, Mubarak Dirar Abd Allah,2015, Derivation of Schrodinger and Einstein Energy Equations from Maxwell's Electric Wave Equation, IOSR Journal of Applied Physics (IOSR-JAP) , Volume 7, Issue 2 Ver. II ,PP 82-87
-Ward, 2008, How to Derive the Schrodinger Equation, Am.J.ph
-Nilesh P Barde, Sandeep D. Patil, Pravin M. Kokne, Pranav P. & Bardapurkar (2015) Deriving Time Dependent Schrodinger Equation from wave Mechanics, Schrodinger Time Independent Equation, Classical and Hamilton-Jacobi Equations. Leonardo Electronic Journal of Practices and Technologies. pp: 31-48.
-Pranab Rudra Sarma, 2011, Direct Derivation of Schrodinger Equation from Hamilton-Jacobi Equation using Uncertainty Principle, Rom. Journ. Phys., Vol. 56, Nos. 9–10, P. 1053–1056, Bucharest.
-Hye Jung Kang,2018, A New Approach for Introducing Schrödinger’s Equation Using Maxwell’s Equations, Quantum Mechanics, and Special Relativity, American Journal of Educational Research, Vol. 6, No. 7, 963-966.
-J.H. Field.2004 “Relationship of quantum mechanics to classical electromagnetism and classical
relativistic mechanics,” Eur. J. Phys. 25, 385-397 .
محمد,.2002 مدخل إلي فلسفة العلوم. الطبعة الخامسة .مركز دراسات الوحدة العربية. بيروت ص ص 365-374 الجابري-10
-Shivam Prabhakaran, 2009. Quantum Mechanics. Book Enclave Jaipur. India.17-24
-Zettili, Nouredine., 2009. Quantum Mechanics: concepts and applications. A John Wiley and Sons, Ltd., Publication. pp 1-4.
-Daniel R. Bes, .2012 Quantum Mechanics, A Modern and Concise Introductory Course. Springer-Verlag Berlin Heidelberg.pp 259-267
-M A de Gosson,.2001.The Principles of Newtonian and Quantum Mechanics..The Need for Planck's constant, h. Imperial College Press.pp 13-17.
-Griffiths, D. J., 2013 Introduction to Electrodynamics, 4th ed, Pearson.pp: 393-394 .
-Helliwell, T. M., 2010. Special Relativity, University Science Books, pp:146-150.
-المدخل إلى ميكانيكا الكم, ر.ديكة , و ج. ويتكه. 1993م , ترجمة آحو يوسف, المركز العربي للتعريف والترجمة والتأليف والنشر , دمشق . ص ص 55-59 .
- نبيل البكري, صلاح البكري2005, ميكانيكا الكم , الطبعة الأولى, دار الفكر العربي , القاهرة ص ص 45-55
- Giancoli, D. C., 2009. Physics for Scientists & Engineers with Modern Physics, 4th ed, Pearson Prentice Hall, Upper Saddle River , 1018-1019.
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