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My conclusion is because I use ##p^4=p^2p^2## to arrive at the error expression for ##p^4##, I cannot later use that expression to argue or conclude that ##p^4\neq p^2p^2##.fresh_42 said:I see the first two equalities, but not your conclusion. Remember that ##\hat{p}^2f## means ##\hat{p}^2(f)##. So why should the two terms in the middle be zero?
Did you work with the approximations for ##\psi_{n00}## or do you have an exact expression?
The two terms in the middle simplifies to ##r^2(2-\frac{r}{a})e^{-3r/2a}##, ignoring any constant factor.
I used ##g=\frac{1}{\sqrt{\pi}}(\frac{1}{a})^{3/2}e^{-r/a}## and ##f=\frac{1}{4\sqrt{2}\pi}(\frac{1}{a})^{3/2}(2-\frac{r}{a})e^{-r/2a}##.
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