Abstract
We use the language developed in Chap. 4 to give a mathematically rigorous formulation of the rules of Quantum Mechanics. The aim is to provide the theoretical instruments to study elementary quantum mechanical problems. We also add some comments and explanations to clarify the meaning of the rules and we mention the foundational problem connected with the measurement process. We conclude describing the approach to a quantum mechanical problem from the point of view of Mathematical Physics.
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Notes
- 1.
Roughly speaking, the space \({\mathscr {H}}_1 \otimes {\mathscr {H}}_2\) is constructed as follows. Let \(\{\phi _j\}\), \(\{\xi _k\}\) be two orthonormal bases in \({\mathscr {H}}_1\) and \({\mathscr {H}}_2\) and consider the set of pairs \(\{ \varPhi _{jk} \} =\{ \phi _j \otimes \xi _k \}\). Then, a generic element of \(\,{\mathscr {H}}_1 \otimes {\mathscr {H}}_2\,\) is \(\,\varPhi = \sum _{jk} c_{jk} \phi _j \otimes \xi _k\), where \(c_{jk}\in \mathbb {C}\,\) and \(\,\sum _{jk} |c_{jk}|^2 < \infty \).
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Teta, A. (2018). Rules of Quantum Mechanics. In: A Mathematical Primer on Quantum Mechanics. UNITEXT for Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-77893-8_5
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DOI: https://doi.org/10.1007/978-3-319-77893-8_5
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