2002/05/31 by Gerhard Groessing
Physics and Astronomy · #quant-ph
published as Substantially corrected version: quant-ph/0311109, Foundations of Physics Letters 17, 4 (2004) 343 - 362 · 11 pages; improved and extended version thanks to very useful referee Reports
arxiv created 2002/08/27 · arxiv updated 2009/12/01
The Schroedinger- and Klein-Gordon equations are directly derived from classical Lagrangians. The only inputs are given by the discreteness of energy (E=hbar.w) and momentum (p=hbar.k), respectively, as well as the assumed existence of a space-pervading field of "zero-point energy" (E0=hbar.w/2 per spatial dimension) associated to each particle of energy E. The latter leads to an additional kinetic energy term in the classical Lagrangian, which alone suffices to pass from classical to quantum mechanics. Moreover, Heisenberg's uncertainty relations are also derived within this framework, i.e., without referring to quantum mechanical or other complex-numbered functions.