Question

Expected value and uncertainty

The uncertainty $\sigma _{O}$ for the expected value of an observable O is calculated as

The expected value is $\left \langle \widehat{O} \right \rangle$ of the operator $\widehat{O}$ with a normalized, one-dimensional one Wave function $\Psi (x)$ given by:

a) Show that

b) Show that , if $\Psi (x)$ is an eigenfunction of the operator $\widehat{O}$ .

Answer 1

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T () Số : 6 - Kổ > (so : (ổ - kô ) 2 2 - Ô <.> - < > Ô +(632 = 8² kôs öt <ås? B (5012 = 22 - 28 rås + <63² toking expectation values of (Sc) operator <8023 = <0² - 2 ô xês + <632) - 14 | 3* - Rổ<ó 2 + 6x + 4) = <u162163 - dôs <H10193 + <w kô3214> - Közs - a<åse + cos2 | = 6+) - > <80²) = cô²> - <ôs? (b) <WIỔIV) = xoxunus = {ôs <41074) = cos*4143 = xôs? using in equation - Go - Ŝo) = seos? - <oj2 cs Scanned with gozo E proved = 0 Scanned with CamScanner - O E proved

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