SOLUTIONS TO THE POSTULATE OF ELEMENTARY PARTICLES-RELATED SCHRÖDINGER TRAVELLING WAVE DIFFERENTIAL EQUATION WITHIN MINKOWSKI SPACES
A. YUMAK *
Department of Physics, Faculty of Arts and Sciences, Marmara University, 34722 Göztepe, Istanbul, Turkey.
K. BOUBAKER *
Unité de Physique des Dispositifs à Semi-conducteurs, Tunis EL MANAR University, Tunisia.
U. YAHSI
Department of Physics, Faculty of Arts and Sciences, Marmara University, 34722 Göztepe, Istanbul, Turkey.
*Author to whom correspondence should be addressed.
Abstract
In this paper, we present a computed solution of partial differential equations for the wave-packets in the Minkowski 4-dimensional spaces, outlining relationship with the Schrödinger equation for the elementary particles. We try to show, through computed results that the Schrödinger equation does not describe the propagation of a single wave- packet of an elementary particle but to the stream of particles. Because of that it has only a statistical meaning that can be applied to the stream of particles and discuss its common probabilistic interpretation and application to a single particle. That is, it is not a wave description of a single particle, but represents only its probabilistically determined position in a given space. Investigations on travelling wave solutions gave evidence to the possibility of implementing continuous solutions for a quantum-based problem.
Keywords: Schrödinger equation, non-relativistic electron, quantum well, Boubaker polynomials expansion scheme BPES, computed solutions, rogue-langmuir traveling wave