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**DiscreteW** Okay, how is this:

We have: $\displaystyle \int_{-\infty}^{\infty} |\psi(x,t)|^2 dx = \int_{-\infty}^{\infty} |Ce^{\frac{-x^2}{2}}e^{\frac{-iEt}{\bar{h}}}|^2 dx = 1,$

$\displaystyle \int_{-\infty}^{\infty}\left[Ce^{\frac{-x^2}{2}}e^{\frac{-iEt}{\bar{h}}}\right]\left[Ce^{\frac{-x^2}{2}}e^{\frac{iEt}{\bar{h}}}\right]\, dx = 1$

$\displaystyle \int_{-\infty}^{\infty} {C}^{2} \left( {e^{-1/2\,{x}^{2}}} \right) ^{2}{e^{-{\frac {{\it iEt}}{h}}}}{e^{{\frac {{\it iEt}}{h}}}}\, dx = 1$

$\displaystyle \int_{-\infty}^{\infty} {C}^{2} \left( {e^{-1/2\,{x}^{2}}} \right) ^{2}\, dx = 1$

$\displaystyle \int_{-\infty}^{\infty} {C}^{2}e^{-x^2} \, dx = 1$

$\displaystyle c^2\sqrt{\pi} = 1$

$\displaystyle \implies c = \pm \frac{1}{\pi^{\frac{1}{4}}}$

Yay? Nay? I was fortunate that the t dropped out, or I wouldn't know how to solve it. I'm going to hope the same happens when I solve for <x> and <p>.

EDIT: Okay, solved for <x>, although not sure if it's right.

$\displaystyle \displaystyle <x> = \int_{-\infty}^{\infty} |\psi(x,t)|^2 x dx \implies \int_{-\infty}^{\infty} |Ce^{\frac{-x^2}{2}}e^{\frac{-iEt}{\bar{h}}}|^2 x dx$

$\displaystyle \int_{-\infty}^{\infty} {C}^{2}e^{-x^2}x \, dx$

$\displaystyle = 0$

Can anyone confirm if this is right?

I need help with the set-up for <p> please!

Are we meant to use the C I found in the first part for <x> and <p>? How should I attack the sketching part? I have the problem with there being too many variables.