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Occupation (or particle) number operator. Eigenvalues and eigenvectors. [closed]

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0 $begingroup$ https://homepage.univie.ac.at/reinhold.bertlmann/pdfs/T2_Skript_Ch_5.pdf Help me please. I made a screen (below) from the article above and highlighted what I did not understand. Why is it true? enter image description here ordinary-differential-equations eigenvalues-eigenvectors quantum-mechanics share | cite | improve this question asked Dec 13 '18 at 12:20 Иван Петров Иван Петров 6 1 $endgroup$ closed as off-topic by Brahadeesh, amWhy, TMM, José Car

To find the mean and variance with given conditions

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0 $begingroup$ $X$ follows normal distribution $mathcal{N}(mu , sigma^2)$ with pdf $f$ and cdf $F$ . If $max_x f(x)= 0.997356$ and $F(-1)+F(7)=1$ , determine $mu, sigma^2$ and $mathbb{P}[Xle 0]$ . I have no clue about this question and unable to interpret the given conditions. How can I relate the max pdf to find the mean. Even if I get to know the first part I can calculate the rest. Any help would be grateful. probability-distributions normal-distribution share | cite | improve this question edited Dec 13 '18 at 12:27 gt6989b 34k 2 24 55