THE SCHRÖDINGER NONLINEAR PARTIAL DIFFERENTIAL EQUATION SOLUTION IN QUANTUM PHYSIC BY NEW APPROACH AYM

Authors

  • MOHAMMAD REZA AKBARI Faculty of Chemical Engineering, University of Tehran, Tehran, Iran.
  • SARA AKBARI Faculty of Chemical Engineering, Islamic Azad University, Ghaemshahr, Iran.
  • ESMAEIL KALANTARI Faculty of Chemical Engineering, Islamic Azad University, Ghaemshahr, Iran.

Keywords:

new method, Akbari-Yasna-Method (AYM), Schrödinger Equation, nonlinear partial differential equation, quantum mechanical

Abstract

In this paper, we investigate and solve a complicated highly nonlinear differential equations of Schrödinger equation by analytical solving of new method which we named it AYM (Akbari Yasna’s Method). The Schrödinger equation is the fundamental equation of physics for describing quantum mechanical behavior. It is also often called the Schrödinger wave equation, and is a partial differential equation that describes how the wave function of a physical system evolves over time. The Schrödinger equation, the fundamental equation of the science of submicroscopic phenomena known as quantum mechanics. And the Schrödinger equation gives exact solutions only for nuclei with one electron: H, He+, Li2+, Be3+, B4+, C5+, etc.The equation, developed (1926) by the Austrian physicist Erwin Schrödinger, has the same central importance to quantum mechanics as Newton’s laws of motion have for the large-scale phenomena of classical mechanics.

References

Ahmadi, A., Akbari, M., Ganji, D.D. (2015): Nonlinear Dynamic in Engineering by Akbari-Ganji's Method. – Xlibris 398p.

Akbari, M.R., Akbari, S., Kalantari, E., Ganji, D.D. (2020a): Akbari-Ganjis method AGM to chemical reactor design for non-isothermal and non-adiabatic of mixed flow reactors. – Journal of Chemical Engineering and Materials Science 11(1): 1-9.

Akbari, M.R., Akbari, S., Kalantari, E. (2020b): Chemical Reactors Catalyst bed and Analytical Solution of Complicated Partial Nonlinear Differential Equations by new Approach AKLM. – Archives in Biomedical Engineering & Biotechnology 5(1): 7p.

Akbari, M.R., Akbari, S., Kalantari, E. (2020c): A study about Exothermic Chemical Reactor by ASM approach strategy. – Determinations in Nanomedicine & Nanotechnology 1(5): 3p.

Akbari, M.R., Ganji, D.D., Nimafar, M., Ahmadi, A.R. (2014a): Significant progress in solution of nonlinear equations at displacement of structure and heat transfer extended surface by new AGM approach. – Frontiers of Mechanical Engineering 9(4): 390-401.

Akbari, M.R., Ganji, D.D., Majidian, A., Ahmadi, A.R. (2014b): Solving nonlinear differential equations of Vanderpol, Rayleigh and Duffing by AGM. – Frontiers of Mechanical Engineering 9(2): 177-190.

Akbari, M.R., Ganji, D.D., Goltabar, A.R. (2014c): Dynamic Vibration Analysis for Non-linear Partial Differential Equation of the Beam–Columns with Shear Deformation and Rotary Inertia by AGM. – Dev Appl Oceanic Eng (DAOE) 3: 22-31.

Akbari, M.R., Ganji, D.D., Ahmadi, A.R., Kachapi, S.H.H. (2014d): Analyzing the nonlinear vibrational wave differential equation for the simplified model of Tower Cranes by Algebraic Method. – Frontiers of Mechanical Engineering 9(1): 58-70.

Akbari, M.R., Nimafar, M., Ganji, D.D., Akbarzade, M.M. (2014e): Scrutiny of non-linear differential equations Euler-Bernoulli beam with large rotational deviation by AGM. – Frontiers of Mechanical Engineering 9(4): 402-408.

Briggs, J.S., Rost, J.M. (2001): On the derivation of the time-dependent equation of Schrödinger. – Foundations of Physics 31(4): 693-712.

He, J.H. (2008): An improved amplitude-frequency formulation for nonlinear oscillators. – International Journal of Nonlinear Sciences and Numerical Simulation 9(2): 211-212.

He, J.H. (1999): Homotopy perturbation technique. – Computer methods in applied mechanics and engineering 178(3-4): 257-262.

He, J. (1998): Approximate analytical solution of Blasius' equation. – Communications in Nonlinear Science and Numerical Simulation 3(4): 260-263.

Ren, Z.F., Liu, G.Q., Kang, Y.X., Fan, H.Y., Li, H. M., Ren, X.D., Gui, W.K. (2009): Application of He's amplitude–frequency formulation to nonlinear oscillators with discontinuities. – Physica Scripta 80(4): 045003.

Rostami, A., Akbari, M., Ganji, D., Heydari, S. (2014): Investigating Jeffery-Hamel flow with high magnetic field and nanoparticle by HPM and AGM. – Open Engineering 4(4): 357-370.

Downloads

Published

2021-04-06

How to Cite

AKBARI, M. R., AKBARI, S., & KALANTARI, E. (2021). THE SCHRÖDINGER NONLINEAR PARTIAL DIFFERENTIAL EQUATION SOLUTION IN QUANTUM PHYSIC BY NEW APPROACH AYM. Quantum Journal of Engineering, Science and Technology, 2(2), 40–46. Retrieved from https://qjoest.com/index.php/qjoest/article/view/23

Issue

Section

Articles