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It was von Neumann’s insight [1] that Heisenberg’s abstract approach to quantum mechanics, which eventually lead to its the standard formulation, finds its mathematical support in operator theory (OT), in the theory of densely-defined, linear and self-adjoint operators (DLSO’s) in Hilbert spaces. In particular, the description and interpretation of the result of the measurement process in quantum theory are closely linked to the spectral theorems for DLSO’s, see, e.g., Sect.  A.3.5 in the Appendix.

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Introduction

  • 章节

  • 发表日期：

    2025年

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  • Horst R. Beyer

摘要

It was von Neumann’s insight [1] that Heisenberg’s abstract approach to quantum mechanics, which eventually lead to its the standard formulation, finds its mathematical support in operator theory (OT), in the theory of densely-defined, linear and self-adjoint operators (DLSO’s) in Hilbert spaces. In particular, the description and interpretation of the result of the measurement process in quantum theory are closely linked to the spectral theorems for DLSO’s, see, e.g., Sect.  A.3.5 in the Appendix.