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Eurasian Journal of Physics,Chemistry and Mathematics

Derivation of Schrodinger Equation from Maxwell Electric Equation

Sami Abdalla Elbadawi

Published May 15, 2022• 0 citations
OpenAlex

Abstract

Maxwell's equations can be used to derive Schrodinger equation. The polarization term is used to find the energy term. One can use plank quantum hypothesis beside Einstein mass energy relation to find a useful expression for Maxwell electric equation. Replacing the electric field intensity by the wave function one found Schrodinger quantum equation.

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Maxwell's equations can be used to derive Schrodinger equation. The polarization term is used to find the energy term. One can use plank quantum hypothesis beside Einstein mass energy relation to find a useful expression for Maxwell electric equation. Replacing the electric field intensity by the wave function one found Schrodinger quantum equation.
The Schrödinger equation: the quantum description of one massive, slow-moving particle To establish a probability wave equation for one photon, it was useful to note that probability density and electromagnetic energy density were proportional. The governing equation for EM radiation fields is the Maxwell wave equation, which is also the governing equation for photon probability wave functions. Converting from EM radiation to photon information is made plausible by identifying energy and momentum operators with time- and space-derivatives, respectively. Thus, the Maxwell wave equation can be interpreted as being equivalent to the energy-momentum relation for photons. Though we don’t have a “Maxwell wave equation” to start with for massive particles, we do have an energy-momentum relation, so borrowing the energy and momentum operators from photons leads to an analogous wave equation for massive particles.
Maxwell equation for the electric field has been solved for any medium by suggesting the wavenumber and angular frequency be complex quantities. This accounts for the field decay by interaction with the medium.This expression for the time and special decay of the electric field in a medium is used to construct a new wave function sensitive to the medium physical properties. This new wave function, unlike the conventional one, differentiates between a beam of particles in a vacuum and that enters a medium which is an attenuated due to the scattering effect.Another expression for time decaying electric field was obtained using Newton’s laws for frictional medium. This expression shows that the electric field diminishes due to friction.Fortunately, this time decaying part of the electric field is typical to that derived from Maxwell’s equations. Finally, a new Schrodinger equation sensitive to the medium properties was derived. This equation, fortunately, describes some scattering processes for Protein scattering, scattering of x-rays, opto-acoustic phonons, and Raman scattering for some materials successfully .
Maxwell equation for the electric field has been solved for any medium by suggesting the wavenumber and angular frequency be complex quantities. This accounts for the field decay by interaction with the medium. This expression for the time and special decay of the electric field in a medium is used to construct a new wave function sensitive to the medium physical properties. This new wave function, unlike the conventional one, differentiates between a beam of particles in a vacuum and that enters a medium which is an attenuated due to the scattering effect. Another expression for time decaying electric field was obtained using Newton’s laws for frictional medium. This expression shows that the electric field diminishes due to friction. Fortunately, this time decaying part of the electric field is typical to that derived from Maxwell’s equations. Finally, a new Schrodinger equation sensitive to the medium properties was derived. This equation, fortunately, describes some scattering processes for Protein scattering, scattering of x-rays, opto-acoustic phonons, and Raman scattering for some materials successfully.
Abstract The Schrödinger equation relates the emergent quantities of wavefunction and electric potential and is postulated as a principle of quantum physics or obtained heuristically. However, physical consistency requires that the Schrödinger equation is a low-energy dynamical condition we can derive from the foundations of quantum electrodynamics. Due to the small value of the electromagnetic coupling constant, we show that the electric potential accurately represents the contributions of intermediate low-energy photon exchanges. Then, from the total nonrelativistic energy relation, we see that the dominant term of the electron wavefunction is a superposition of plane waves that satisfies the Schrödinger equation. Our derivation shows that the Schrödinger equation is not an energy conservation relation because its middle term does not represent the electron kinetic energy as assumed. We analyze the physical content of the Schrödinger equation and verify our assessments by calculating and evaluating the physical quantities in the ground state of the hydrogen atom. Furthermore, we explain why nonrelativistic quantum dynamics differs from classical dynamics. Undergraduate students can follow the derivation because it involves fundamental physical concepts and mathematical expressions, and we explain every step.