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hilbert_space_mean_value [2013/08/31 23:10]
nikolaj
hilbert_space_mean_value [2013/08/31 23:43]
nikolaj
Line 18: Line 18:
   * $\Delta_\psi A = \left(\overline{\left(A-\overline A\right)^2}\right)^\frac{1}{2} = \overline{A^2}-\overline{A}^2=\frac{\Vert(A-\overline A)\psi\Vert}{\Vert\psi\Vert}$ 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
 + 
 +=== Theorems === 
 + 
 +$AB=BA\implies \gamma\in [-1,1]$.
  
 ==== Context ==== ==== Context ====
 === Requirements === === Requirements ===
 [[Hilbert space]] [[Hilbert space]]
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