An Introduction to the Mathematical Structure of Quantum Mechanics pdf epub mobi txt 電子書 下載2025
- 量子力學
- 量子力學
- 數學物理
- 綫性代數
- 希爾伯特空間
- 算符理論
- 量子信息
- 物理學
- 數學
- 理論物理
- 自伴算符
具體描述
This book arises out of the need for Quantum Mechanics (QM) to be part of the common education of mathematics students. Rather than starting from the Dirac?Von Neumann axioms, the book offers a short presentation of the mathematical structure of QM using the C*-algebraic structure of the observable based on the operational definition of measurements and the duality between states and observables. The description of states and observables as Hilbert space vectors and operators is then derived from the GNS and Gelfand?Naimark Theorems. For finite degrees of freedom, the Weyl algebra codifies the experimental limitations on the measurements of position and momentum (Heisenberg uncertainty relations) and Schroedinger QM follows from the von Neumann uniqueness theorem. The existence problem of the dynamics is related to the self-adjointness of the differential operator describing the Hamiltonian and solved by the Rellich?Kato theorems. Examples are discussed which include the explanation
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