Momentum eigenstate

Homework Statement

I am trying to translate what is meant by:
<psi | p | psi>
<psi|p^2|psi>
<psi | x | psi>
In a mathematicaly context as shown by this link:

Can anyone specify what these mean?

Thanks!

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tiny-tim
Homework Helper
hi imagemania!

<| denotes a row vector

|| denotes a matrix

|> denotes a column vector

Ok, but im still not following how he got one for the first question:
<psi | p | psi> = 0

for the integral:
$$\psi = \int_{-\infty}^{\infty} {e}^{-\alpha {(k-{k}_{0})}^{2}}{e}^{ikx} dk$$

Thanks

tiny-tim
Homework Helper
not following you …

ψ is as given, and p is the momentum operator

Perhaps i'll ignore that post and go back to the fundamental question. From my understanding,
$$\bar{p}=\frac{hk}{2 \pi}$$. Knowing $$\psi$$ is there a way to deduce a better answer to $$\bar{p}$$ or is it just as I said here?

I am also unsure about the equation for mean value of x.

Thanks :)

vela
Staff Emeritus
$$\langle \psi | \hat{A} | \psi \rangle = \int \psi^*(x)\hat{A}\psi(x)\,dx$$