2005/10/15 by Agus Budiyono, Agung Budiyono, Budiyono, Agung
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Quantum Mechanics and Applications #Quantum chaos and dynamical systems #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/0510117
content changed, 22 pages
arxiv created 2009/08/19 · arxiv updated 2009/12/01
We consider a mass-less manifestly covariant \it linear Schrödinger equation. First, we show that it possesses a class of non-dispersive soliton solution with finite-size spatio-temporal support inside which the quantum amplitude satisfies the Klein-Gordon equation with finite \it emergent mass. We then proceed to interpret the soliton wave function as describing a particle with finite mass, energy and momentum. Inside the spatio-temporal support, the wave function shows spatio-temporal internal vibration with angular frequency and wave number that are determined by the energy-momentum of the particle as firstly conjectured by de Broglie. Imposing resonance of the internal vibration inside the spatio-temporal support leads to Planck-Einstein quantization of energy-momentum. The first resonance mode is shown to recover the classical energy-momentum relation developed in special relativity. We further show that the linearity of the Schrödinger equation allows one to construct many solitons solution through superposition, each describing a particle with various masses, energies and momenta.