2006/01/12 by Wolfgang Koehler, Koehler, Wolfgang
Physics and Astronomy · #Crystallography and Radiation Phenomena #FOS: Physical sciences #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph) #Quantum and Classical Electrodynamics #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/0601080
41 pages, 1 figure, second revised and extended version
openalex publication_date 2006/01/12 · arxiv created 2006/06/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Here I present a new discrete model of quantum mechanics for relativistic 1-electron systems, in which particle movement is described by a directed space-time graph with attached 4-spinors, but without any continuous wave functions. These graphs only consist of few space-like edges, e.g. the ground state of atoms is described by two nodes and one edge, and interactions only take place at the nodes. The fundament is an extremal principle for a relativistic invariant "Lagrangian sum", from which "field-equations" and "equations of motion" are derived, so the states (including the graph nodes) are completely determined. As important validations of the model, the corresponding graphs for the stationary Dirac-equation for the atom are drawn and the correct spectra are computed (Sommerfeld-levels). Also a discrete Schroedinger approximation and an associated "Hamiltonian sum" are derived and the correct equation of a classical moving particle under Lorentz-force is presented. I hope, that this new approach will help, to overcome some problems of current quantum mechanics by making the wave function superfluous.