- #1

Zero1010

- 40

- 2

- Homework Statement
- I need help writing in Dirac notation

- Relevant Equations
- ##<A>=\int_{-\infty}^\infty \Psi^*(x) \hat A \Psi (x) dx ##

##<A> = <\Psi|\hat A|\Psi>##

##<A^2>=\int_{-\infty}^\infty |\Psi^*(x)|^2 \hat A^2 dx ##

Edited after post below:

Hi,

I need to show that the square of the expectation value of an observable takes a certain form in Dirac notation.

I know in wave notation that the expectation value is a sandwich integral which looks like this:

##<A>=\int_{-\infty}^\infty \Psi^*(x) \hat A \Psi (x) dx ##

Which is written in Dirac notation as:

##<A> = <\Psi|\hat A|\Psi>##

And the expectation value of a squared observable is written as:

##<A^2>=\int_{-\infty}^\infty \Psi^*(x) \hat A^2 \Psi(x) dx ##

But I am not sure how to write this in Dirac notation.

Thanks for any help and hopefully this makes sense.

Hi,

I need to show that the square of the expectation value of an observable takes a certain form in Dirac notation.

I know in wave notation that the expectation value is a sandwich integral which looks like this:

##<A>=\int_{-\infty}^\infty \Psi^*(x) \hat A \Psi (x) dx ##

Which is written in Dirac notation as:

##<A> = <\Psi|\hat A|\Psi>##

And the expectation value of a squared observable is written as:

##<A^2>=\int_{-\infty}^\infty \Psi^*(x) \hat A^2 \Psi(x) dx ##

But I am not sure how to write this in Dirac notation.

Thanks for any help and hopefully this makes sense.

Last edited: