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hilbert_space_mean_value [2013/08/31 23:10] nikolaj |
hilbert_space_mean_value [2013/08/31 23:43] nikolaj |
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* $\Delta_\psi A = \left(\overline{\left(A-\overline A\right)^2}\right)^\frac{1}{2} = \overline{A^2}-\overline{A}^2=\frac{\Vert(A-\overline A)\psi\Vert}{\Vert\psi\Vert}$ is called non-negative mean fluctuation. | * $\Delta_\psi A = \left(\overline{\left(A-\overline A\right)^2}\right)^\frac{1}{2} = \overline{A^2}-\overline{A}^2=\frac{\Vert(A-\overline A)\psi\Vert}{\Vert\psi\Vert}$ is called non-negative mean fluctuation. | ||
- | * $\overline{(A-\overline{A})(B-\overline{B})}/(\Delta A\cdot \Delta B)=(\overline{AB}-\overline{A}\overline{B})/(\Delta A\cdot \Delta B)$ is called the correlation coefficient. | + | * $\gamma=\overline{(A-\overline{A})(B-\overline{B})}/(\Delta A\cdot \Delta B)=(\overline{AB}-\overline{A}\overline{B})/(\Delta A\cdot \Delta B)$ is called the correlation coefficient. |
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+ | === Theorems === | ||
+ | |||
+ | $AB=BA\implies \gamma\in [-1,1]$. | ||
==== Context ==== | ==== Context ==== | ||
=== Requirements === | === Requirements === | ||
[[Hilbert space]] | [[Hilbert space]] |