Wavefunction normalisation and expectation values

[MoAli]

Homework Statement

See Image, Sorry Its easier for me to attach images than writing all equation on the forum's keyboard!

I only need to check if I'm working it out correctly up to the position expectation value because I don't want to dive in the rest on wrong basis !

Homework Equations

The Attempt at a Solution

 

[PeroK]

You need to try some latex. What you have is correct, except that right at the end in the expected value of $x$, $\alpha$ leapt from the denominator to the numerator.

$\langle x \rangle = \frac{12}{13 \alpha}$

 

[MoAli]

Yeah still trying to learn latex, anyway, where the question asks to prove momentum expectation value is zero without integrals I get stuck, I got <p^2> = \frac{12/h^2}{13 } which still doesn't make sense to me, the units don't work!

 

[PeroK]

Yeah still trying to learn latex, anyway, where the question asks to prove momentum expectation value is zero without integrals I get stuck, I got the \langle p^2 \rangle to be \frac{12h^2}{72}

Regarding $\langle p \rangle$ you might like to think about complex numbers and expectation values.

I haven't tried to calculate $\langle p^2 \rangle$ or $\langle x^2 \rangle$. You just need to be careful with the integration.