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Gianfranco (talk | contribs) (Created page with "===3.2. Von Neumann formalism for quantum observables=== In the original quantum formalism (Von Neumann, 1955), physical observable <math>A</math> is represented by a Hermitian operator <math>\hat{A}</math> . We consider only operators with discrete spectra:<math>\hat{A}=\sum_x x\hat{E}^A(x)</math> where <math>\hat{E}^A(x)</math> is the projector onto the subspace of <math display="inline">\mathcal{H}</math> corresponding to the eigenvalue <math display="inline">x</...") |
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===3.2. Von Neumann formalism for quantum observables=== | ===3.2. Von Neumann formalism for quantum observables=== | ||
In the original quantum formalism (Von Neumann, 1955), physical observable <math>A</math> is represented by a Hermitian operator <math>\hat{A}</math> . We consider only operators with discrete spectra:<math>\hat{A}=\sum_x x\hat{E}^A(x)</math> where <math>\hat{E}^A(x)</math> is the projector onto the subspace of <math display="inline">\mathcal{H}</math> corresponding to the eigenvalue <math display="inline">x</math>. Suppose that system’s state is mathematically represented by a density operator<math display="inline">\rho</math>. Then the probability to get the answer <math display="inline">x</math> is given by the Born rule | In the original quantum formalism (Von Neumann, 1955),<ref>Von Neumann J. | ||
Mathematical Foundations of Quantum Mechanics | |||
Princeton Univ. Press, Princeton, NJ, USA (1955) | |||
Google Scholar</ref> physical observable <math>A</math> is represented by a Hermitian operator <math>\hat{A}</math> . We consider only operators with discrete spectra:<math>\hat{A}=\sum_x x\hat{E}^A(x)</math> where <math>\hat{E}^A(x)</math> is the projector onto the subspace of <math display="inline">\mathcal{H}</math> corresponding to the eigenvalue <math display="inline">x</math>. Suppose that system’s state is mathematically represented by a density operator<math display="inline">\rho</math>. Then the probability to get the answer <math display="inline">x</math> is given by the Born rule | |||
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