Electromagnetic Interaction in the Schrodinger Equation Model

A. J. de Faria, H. M. França, G. G. Gomes +1 more

Khalid Md. Nor, Ithnin Abdul Jalil, Hassan Abu Kasim

The relativistic Schrodinger equation is reinterpreted as describing a classical particle that mutually-interacts with other objects via electromagnetic-like gravity waves. The accompanying derivation equates the usual quantum mechanical energy and momentum operators to the effects of negative or attractive energy. Lorentz-like transformation equations are obtained that yield the uncertainty principle such that quantum uncertainty is ascribed to the disregard of a magnetic-like component of a gravity wave. Finally, quantum-level Maxwell-like equations that involve the above gravity waves are derived.

M. A. Rego-Monteiro, E. M. F. Curado

We construct a new nonlinear deformed Schrödinger structure using a nonlinear derivative operator which depends on a parameter $q$. This operator recovers Newton derivative when $q \rightarrow 1$. Using this operator we propose a deformed Lagrangian which gives us a deformed nonlinear Schrödinger equation with a nonlinear kinetic energy term and a standard potential $V(\vec{x})$. We analytically solve the nonlinear deformed Schrödinger equation for $V(\vec{x}) = 0$ and $q \simeq1$. This model has a continuity equation, the energy is conserved, as well as the momentum and also interacts with electromagnetic field. Planck relation remains valid and in all steps we easily recover the undeformed quantities when the deformation parameter goes to 1. Finally, we numerically solve the equation of motion for the free particle in any spatial dimension, which shows a solitonic pattern when the space is equal to one for particular values of $q$.

Zbigniew Haba

Ivan Gonoskov, G. A. Vugalter, Vyacheslav A. Mironov

Using the analytically obtained solution of the Schrödinger equation for an electron in a quantized electromagnetic field, the ionization of an atom has been considered in the framework of a simple one-dimensional model. Expressions for the ionization rate and photoelectron spectrum have been derived and analyzed. We discuss a difference between the results obtained in the model in which the electromagnetic field is described classically and the results obtained in the model of quantized electromagnetic field. In particular, in the latter model the photoelectron spectrum can have a minimum at a certain number of absorbed photons. The minimum is a consequence of destructive interference between the contributions of two parts of the interaction operator.