From Physics to Mathematics
From Physics to Mathematics
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从物理到数学
DOI：
10.1007/b99978_12
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发表时间：
2009
期刊：
影响因子：
--
通讯作者：
S. Teufel
中科院分区：
文献类型：
--
作者：
D. Dürr;S. Teufel
量子力学的基础涉及希尔伯特空间，希尔伯特空间上的线性算子，酉算子，自伴算子及其谱。玻姆力学的基础并不包含这类内容，而且这类内容似乎也不相关。当然，薛定谔方程是一个偏微分方程，包含微分算子，但麦克斯韦-洛伦兹电磁理论也是如此，人们学习电磁理论时不需要所有这些抽象概念。为什么量子力学不同？为什么它需要基于如此抽象的数学概念？
The foundations of quantum mechanics are concerned with Hilbert spaces, linear operators on Hilbert spaces, unitary operators, and self-adjoint operators and their spectra. The foundations of Bohmian mechanics contain nothing of that sort and nothing of that sort seems relevant. Of course, the Schrödinger equation is a partial differential equation and contains differential operators, but so does the Maxwell– Lorentz theory of electromagnetism, which one learns about without all those abstract notions. Why is quantum mechanics different? Why does it need to be based on such abstract mathematical notions?