Derivation of the Schroedinger Equation and the Klein-Gordon Equation from First Principles

Details Derivation of the Schroedinger Equation and the Klein-Gordon Equation from First Principles Derivation of the Schroedinger Equation and the Klein-Gordon Equation from First Principles

2002-05-09

arxiv.org/abs/quant-ph/0205047v6

Substantially corrected version: quant-ph/0311109, Foundations of Physics Letters 17, 4 (2004) 343 - 362

Physics

Quantum Physics

11 pages; improved and extended version thanks to very useful referee Reports

Scientific paper

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" (E_0=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.

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