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arXiv 0810.2394quant-ph
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量子力学的统计起源

The statistical origins of quantum mechanics

U. Klein

备注：
slightly modified version, 24 pages, no figures
发表信息：
Physics Research International, vol. 2010, Article ID 808424, http://www.hindawi.com/journals/phys/2010/808424.html
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摘要：

结果表明，薛定谔方程可由三个公设导出。第一种是经典力学的一种统计变形，由粒子力学的正则方程通过用统计平均值替换所有可观测量而得到的一组两个关系。第二种是概率流的局部守恒定律，其形式为梯度。第三种是最大无序原则，这是由最小Fisher信息要求实现的。计算期望值的规则是从第四个假设，即平均能量守恒的要求得到的。量子理论的所有这些基本关系都可以从具有统计性质的前提导出，这一事实被解释为支持量子力学的统计解释的有力论据。比较了量子理论和经典统计理论的结构，指出了它们之间的一些根本区别。

英文摘要：

It is shown that Schroedinger's equation may be derived from three postulates. The first is a kind of statistical metamorphosis of classical mechanics, a set of two relations which are obtained from the canonical equations of particle mechanics by replacing all observables by statistical averages. The second is a local conservation law of probability with a probability current which takes the form of a gradient. The third is a principle of maximal disorder as realized by the requirement of minimal Fisher information. The rule for calculating expectation values is obtained from a fourth postulate, the requirement of energy conservation in the mean. The fact that all these basic relations of quantum theory may be derived from premises which are statistical in character is interpreted as a strong argument in favor of the statistical interpretation of quantum mechanics. The structures of quantum theory and classical statistical theories are compared and some fundamental differences are identified.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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