Related papers: How to Derive the Schrodinger Equation
Although the nonlinear Schrodinger equation description of Einstein spaces has provided insights into how quantum mechanics might modify the classical general relativistic description of space-time, an exact quantum description of…
Ehrenfest theorem is proven in relativistic quantum theory of charged particles, moving under the influence of an external electromagnetic field. In order to extend the classic Ehrenfest result to the relativistic domain we bypassed the…
Individual quantum objects display inseparable coexisting wave-like properties and particle-like properties; such inseparable coexistence can seem paradoxical and mind-boggling. The apparent paradox is resolved by the unified theory of…
In this note we solve theoretically the Schrodingers differential equation using results based on our previous work which concern semigroup operators. Our method does not use eigenvectors or eigenvalues and the solution depends only from…
An isotropic electromagnetic field in a plasma of thermalized electrons undergoes changes in energy as a result of Compton scattering and an Einstein-Hopf drag force on the electrons, eventually approaching a Bose-Einstein photon…
Light waves carry along their own gravitational field; for simple plain electromagnetic waves the gravitational field takes the form of a pp-wave. I present the corresponding exact solution of the Einstein-Maxwell equations and discuss the…
Schrodinger equation for a charged particle interacting with the plane wave electromagnetic field is solved exactly. The exact analytic solution and the perturbative solution up to second order are compared.
We set up the Maxwell's equations and the corresponding classical wave equations for the electromagnetic waves which together with the generating source, a traveling oscillatory charge of zero rest mass, comprise a particle traveling in the…
We propose a simple relativistic derivation of the electric and the magnetic fields generated by an electric point charge moving with constant velocity. Our approach is based on the radar detection of the point space coordinates where the…
We classify (1+3)-dimensional Schr\"odinger equations for a particle interacting with the electromagnetic field that are solvable by the method of separation of variables. As a result, we get eleven classes of the electromagnetic vector…
We derive the Schroedinger equation for a spinless charged particle constrained to a curved surface with electric and magnetics fields applied. The particle is confined on the surface using a thin-layer procedure, giving rise to the…
The method of separation of variables is shown to apply to both the classical and quantum Neumann model. In the classical case this nicely yields the linearization of the flow on the Jacobian of the spectral curve. In the quantum case the…
We combine Maxwell's equations with Eulers's equation, related to a velocity field of an immaterial fluid, where the density of mass is replaced by a charge density. We come out with a differential system able to describe a relevant…
Classical statistical particle mechanics in the configuration space can be represented by a nonlinear Schrodinger equation. Even without assuming the existence of deterministic particle trajectories, the resulting quantum-like statistical…
According to the widely accepted notion, the Schr{\"o}dinger equation (SE) is not derivable in principle. Contrary to this belief, we present here a straightforward derivation of SE. It is based on only two fundamentals of mechanics: the…
The Lorentz Transformation is derived from only three simple postulates: (i) a weak kinematical form of the Special Relativity Principle that requires the equivalence of reciprocal space-time measurements by two different inertial…
A numerical-relativity calculation yields in general a solution of the Einstein equations including also a radiative part, which is in practice computed in a region of finite extent. Since gravitational radiation is properly defined only at…
The classical relativistic wave equations are presented as partial difference equations in the arena of covariant discrete phase space. These equations are also expressed as difference-differential equations in discrete phase space and…
This is the first in a series Of papers in which we initiate the study Of very rough solutions to the initial value problem for the Einstein Vacuum equations expressed relative to wave coordinates. By very rough we mean solutions which…
We show that equation for radial wave function in its traditional form is compatible with the full Schrodinger equation if and only if a definite additional constraint required. This constraint has a boundary condition form at the origin.…