Question

What am i doing wrong here,

Answer 1

Everything looks good. You've got some nasty fractions to deal with in there.

Answer 2

Take a look at the expanded form presented here: http://www.wolframalpha.com/input/?i=%283%2Fb%29%28%28a%5E2%2F4%29+%2B+%281%2F%28b-a%29%5E2%29%281%2F12%29%28b%5E4+-+a%5E2%286b%5E2+-+8ba+%2B+3a%5E2%29%29%29

It might help.

Answer 3

Is that a two-dimensional wave in the problem? Because I've never seen the formula:
\[<x >=\int\limits_{-\infty}^{\infty}x \left| \Psi ^{2} \right|dx\]

Answer 4

well i am guessing that is because you haven't studied Quantum Mechanics @Mani_Jha

In QM the probability a particle of the position of x being between a and b can be written
\[ P_{a≤x≤b}=\int\limits_{a}^{b}\rho(x,t) \text{d}x\]
rho is the probability density
\[\rho(x,t)= \int\limits_{a}^{b}|\Psi|^2\text{d}x\] where\[ | \Psi^2|=|\Psi^*\Psi|=\langle \Psi| \Psi \rangle \]

the expectation value of x (ie the mean/average)
\[\langle x \rangle = \int\limits_{-\infty}^\infty x | \Psi |^2 \text{d} x\]

Answer 5

Thanks, now it makes sense. Actually I studied a bit of quantum mechanics when I was studying the Atomic Structure.
And your process seems all right to me(unless if you've made a calculation mistake in the '......' part which you haven't shown).

Answer 6

the answer at the bottom is the answer in the back of the book
the ... bit is where i i stuck and dont know what to put