Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

International Journal of Science and Research (IJSR)

Spatial Wave Function Diminishing Due to Friction Force

Published Aug 5, 2016• 0 citations
Publisher

Abstract

Schrodinger equation for resistive medium is obtained through momentum operator. This new equation reduces to ordinarySchrodinger equation in the absence of friction.This equation describes spatially decaying wave function when particles are treated as strings.This solution can describe the inelastic scattering process.
DOI
10.21275/art2016884

Related papers

Quantum Wave Function Based on String Theory for Frictional Medium to Obtain Collision Probability, Energy Operator and Schrodinger Equation

Asma Mohamed Elhussin

Schrodinger equation suffer from being not sensitive to the mechanical properties as well as the electric and magnetic properties of matter. This set back can be cured by starting the derivation using the function sensitive to these parameters. Treating particle as vibrating strings a useful expression for the velocity was found using the equation of motion. Then the relation of current density with a velocity and electric field intensity was utilized to obtain the electric field intensity in a frictional medium. Using the analogy of the electric field and quantum wave function, the wave function was obtained and found to give the conventional expression for the collision probability with relaxation time twice the classical one. Another approach was tackled by obtaining a useful expression of the total energy of strings for resistive collisional medium. This expression utilizes the wave function of quantum particle in a frictional medium to obtain collision probability formula. Fortunately this latter approach gives a relaxation time equal to the classical one. The same wave function is used to find Hamiltonian operator for the both steady state and perturbed state by friction. Fortunately both Hamiltonians satisfy hermiticty condition. The hermiticty condition for the perturbed states however needs splitting the Hamiltonian into unpertured and perturbed part.. The perturbed term satisfies uncertainty principle. The energy expression for the resistive medium resembles that of Einstein and RLC circuits. Schrodinger equation for the frictional medium was also found, where it reduces to the ordinary one when friction disappear.

International Journal of Applied Mathematics and Theoretical Physics•Jan 1, 2019•0 citations

Derivation of Time and Spatial Decaying of Schrodinger Equation Using Maxwell Electric Equation to Describe Scattering in Some Physical Systems

Lutfi Mohammed AbdAlgadir, Zoalnoon Ahmed Abeid Allah Saad, HassabAllah Mohamed Abdulgadir +1 more

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 .

•Dec 15, 2020•1 citation

Derivation of Time and Spatial Decaying of Schrodinger Equation Using Maxwell Electric Equation to Describe Scattering in Some Physical Systems

Zoalnoon Ahmed Abeid Allah Saad, Lutfi Mohammed, HassabAllah Moammed +1 more

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.

•Jul 14, 2020•2 citations

Potential Dependent Frictional Schrodinger Equation

Ebtisam A. Mohamed, Mubarak Dirar, Ibrahim Adam Ibrahim Hammad +2 more

By treating particles as harmonic oscillator is obtained the friction energy related to the momentum. The energy and the corresponding Newtonian operator is found. This result in a new Schrodinger equation accounting for the effect of friction. This new equation shows that the energy and mass are quantized, if one treats particles as strings. The radioactive decay law and collision probability is also derived.

American Scientific Research Journal for Engineering, Technology, and Sciences•Jan 7, 2018•2 citations

Scattering of Waves in the Phase Space, Quantum Mechanics, and Irreversibility

E. M. Beniaminov

We give an example of a mathematical model describing quantum mechanical processes interacting with medium. As a model, we consider the process of heat scattering of a wave function defined on the phase space. We consider the case when the heat diffusion takes place only with respect to momenta. We state and study the corresponding modified Kramers equation for this process. We consider the consequent approximations to this equation in powers of the quantity inverse to the medium resistance per unit of mass of the particle in the process. The approximations are constructed similarly to statistical physics, where from the usual Kramers equation for the evolution of probability density of the Brownian motion of a particle in the phase space, one deduces an approximate description of this process by the Fokker-Planck equation for the density of probability distribution in the configuration space. We prove that the zero (invertible) approximation to our model with respect to the large parameter of the medium resistance, yields the usual quantum mechanical description by the Schrodinger equation with the standard Hamilton operator. We deduce the next approximation to the model with respect to the negative power of the medium resistance coefficient. As a result we obtain the modified Schrodinger equation taking into account dissipation of the process in the initial model, and explaining the decoherence of the wave function.

•Jan 1, 2015•2 citations

A Refinement of the Schrödinger Equation Involving Dissipation of Waves in the Phase Space

E. M. Beniaminov

We give an example of a mathematical model describing quantum mechanical processes interacting with medium. As a model, we consider the process of heat scattering of a wave function defined on the phase space. We consider the case when the heat diffusion takes place only with respect to momenta. We state and study the corresponding modified Kramers equation for this process. We consider the consequent approximations to this equation in powers of the quantity inverse to the medium resistance per unit of mass of the particle in the process. The approximations are constructed similarly to statistical physics, where from the usual Kramers equation for the evolution of probability density of the Brownian motion of a particle in the phase space, one deduces an approximate description of this process by the Fokker--Planck equation for the density of probability distribution in the configuration space. We prove that the zero (invertible) approximation to our model with respect to the large parameter of the medium resistance, yields the usual quantum mechanical description by the Schrödinger equation with the standard Hamilton operator. We deduce the next approximation to the model with respect to the negative power of the medium resistance coefficient. As a result we obtain the modified Schrödinger equation taking into account dissipation of the process in the initial model.

arXiv:1312.1619•Dec 5, 2013•0 citations
Schrodinger equation suffer from being not sensitive to the mechanical properties as well as the electric and magnetic properties of matter. This set back can be cured by starting the derivation using the function sensitive to these parameters. Treating particle as vibrating strings a useful expression for the velocity was found using the equation of motion. Then the relation of current density with a velocity and electric field intensity was utilized to obtain the electric field intensity in a frictional medium. Using the analogy of the electric field and quantum wave function, the wave function was obtained and found to give the conventional expression for the collision probability with relaxation time twice the classical one. Another approach was tackled by obtaining a useful expression of the total energy of strings for resistive collisional medium. This expression utilizes the wave function of quantum particle in a frictional medium to obtain collision probability formula. Fortunately this latter approach gives a relaxation time equal to the classical one. The same wave function is used to find Hamiltonian operator for the both steady state and perturbed state by friction. Fortunately both Hamiltonians satisfy hermiticty condition. The hermiticty condition for the perturbed states however needs splitting the Hamiltonian into unpertured and perturbed part.. The perturbed term satisfies uncertainty principle. The energy expression for the resistive medium resembles that of Einstein and RLC circuits. Schrodinger equation for the frictional medium was also found, where it reduces to the ordinary one when friction disappear.
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.
We give an example of a mathematical model describing quantum mechanical processes interacting with medium. As a model, we consider the process of heat scattering of a wave function defined on the phase space. We consider the case when the heat diffusion takes place only with respect to momenta. We state and study the corresponding modified Kramers equation for this process. We consider the consequent approximations to this equation in powers of the quantity inverse to the medium resistance per unit of mass of the particle in the process. The approximations are constructed similarly to statistical physics, where from the usual Kramers equation for the evolution of probability density of the Brownian motion of a particle in the phase space, one deduces an approximate description of this process by the Fokker-Planck equation for the density of probability distribution in the configuration space. We prove that the zero (invertible) approximation to our model with respect to the large parameter of the medium resistance, yields the usual quantum mechanical description by the Schrodinger equation with the standard Hamilton operator. We deduce the next approximation to the model with respect to the negative power of the medium resistance coefficient. As a result we obtain the modified Schrodinger equation taking into account dissipation of the process in the initial model, and explaining the decoherence of the wave function.
We give an example of a mathematical model describing quantum mechanical processes interacting with medium. As a model, we consider the process of heat scattering of a wave function defined on the phase space. We consider the case when the heat diffusion takes place only with respect to momenta. We state and study the corresponding modified Kramers equation for this process. We consider the consequent approximations to this equation in powers of the quantity inverse to the medium resistance per unit of mass of the particle in the process. The approximations are constructed similarly to statistical physics, where from the usual Kramers equation for the evolution of probability density of the Brownian motion of a particle in the phase space, one deduces an approximate description of this process by the Fokker--Planck equation for the density of probability distribution in the configuration space. We prove that the zero (invertible) approximation to our model with respect to the large parameter of the medium resistance, yields the usual quantum mechanical description by the Schrödinger equation with the standard Hamilton operator. We deduce the next approximation to the model with respect to the negative power of the medium resistance coefficient. As a result we obtain the modified Schrödinger equation taking into account dissipation of the process in the initial model.