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从第一性原理推导Schroedinger方程和Klein-Gordon方程

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

Gerhard Groessing

备注：
11 pages; improved and extended version thanks to very useful referee Reports
发表信息：
Substantially corrected version: quant-ph/0311109, Foundations of Physics Letters 17, 4 (2004) 343 - 362
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摘要：

薛定谔方程和克莱因-戈登方程直接从经典拉格朗日方程导出。唯一的输入分别由能量（E=hbar.w）和动量（p=hbar.k）的离散性以及与能量为E的每个粒子相关联的“零点能量”（E_0=hbar.w/2/空间维度）的空间弥漫场的假设存在给出。后者导致了经典拉格朗日量中的一个额外的动能项，仅这一项就足以从经典力学过渡到量子力学。此外，海森堡的不确定性关系也是在这个框架内导出的，即，而不涉及量子力学或其它复数函数。

英文摘要：

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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