Computing Eigenfunctions for a One-Dimensional Operator

[malawi_glenn]

actually, this was written in the post

<br /> &lt; x &gt; = \int _{\text{All space}} \psi^*(x)x\psi(x) dx = \int x|\psi (x)|^2 dx <br />

So I have no clue why you asked. Maybe this is too difficult for you? I suggest you wait. You still don't seem to follow my advise that taking one small step a head =(

 

[NepToon]

i just didnt know the notation. i know the complex conjugate. ok, so here's the question.
for yesterdays O(with hat) i got the eigenfunction(ѱ) after normalization to be,
ѱ=exp((x² -x)/2ih') how would i go on about finding the expectation value of x, p_x and p_x²?
would you mind telling me the process step by step??

 

[malawi_glenn]

I don't think you understand this thing with operators and eigenfunction...

It is a difference of FINDING the eigenfunctions to a given operator and finding the eigenvalues of a given operator on a given wavefunction.

The example was:

Given the wavefuction \psi(x) = (1/(\pi ^{1/4}\sqrt{d}))\exp (ikx - x^2/(2d^2))

Evaluate the expectation values of x, x^2, p and p^2

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So for the first part, <x> is int ѱ* x ѱ dx

What you need to know here are two parts, first what the complex conjugate of ѱ is and then what integral of a Gaussian integral is.

http://en.wikipedia.org/wiki/Gaussian_integral

See " Generalizations "

This is too hard for you, I give up.