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

@article{citeulike:1157636, abstract = {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.}, archivePrefix = {arXiv}, author = {Groessing, G.}, citeulike-article-id = {1157636}, citeulike-linkout-0 = {http://arxiv.org/abs/quant-ph/0205047}, citeulike-linkout-1 = {http://arxiv.org/pdf/quant-ph/0205047}, citeulike-linkout-2 = {http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=2002quant.ph..5047G}, eprint = {quant-ph/0205047}, journal = {ArXiv Quantum Physics e-prints}, keywords = {abstract-machines, all-physical-theories, all-possible-physical-theories, all-possible-wave-equations, axiomatic, axiomatics, category-of-theories, discrete-symbol-manipulation, equations, extremal-physics, first-principles, formal-physics, fundamental-principles, klein-gordon-equation, lagrangians, lattice-of-equations, mathematical-physics, physical-theories, principles, schroedinger-equation, synthetic-physics, theoretical-physics, wave-equations}, month = {May}, posted-at = {2009-05-30 18:52:39}, priority = {2}, title = {Derivation of the Schroedinger Equation and the Klein-Gordon Equation from First Principles}, url = {http://arxiv.org/abs/quant-ph/0205047}, year = {2002} }

TY - JOUR ID - citeulike:1157636 L3 - citeulike-article-id:1157636 N2 - 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. JF - ArXiv Quantum Physics e-prints TI - Derivation of the Schroedinger Equation and the Klein-Gordon Equation from First Principles KW - abstract-machines KW - all-physical-theories KW - all-possible-physical-theories KW - all-possible-wave-equations KW - axiomatic KW - axiomatics KW - category-of-theories KW - discrete-symbol-manipulation KW - equations KW - extremal-physics KW - first-principles KW - formal-physics KW - fundamental-principles KW - klein-gordon-equation KW - lagrangians KW - lattice-of-equations KW - mathematical-physics KW - physical-theories KW - principles KW - schroedinger-equation KW - synthetic-physics KW - theoretical-physics KW - wave-equations AU - Groessing, G PY - 2002/May// UR - http://arxiv.org/abs/quant-ph/0205047 ER -