Infinite square well. probability isues.

[OGrowli]

(a) Obtain the ground state wave function and energy. Draw the wave function
\psi_{1}(x)
(how many nodes are there in the ground state?) and the probability
\left | \psi_{1}(x) \right |^{2}
of finding the particle in dx about x.

V(x)=\begin{cases}<br /> &amp; \infty,\text{ }x \geq a, x\leq -a \\ <br /> &amp; 0,\text{ } -a&lt; x&lt; a <br /> \end{cases}

I've found the ground state wave function and energy to be:

\psi_{1}(x)=\sqrt{\frac{1}{a}}sin(\frac{\pi}{a}x)
E_{1}=\frac{\hbar^{2}\pi^{2}}{2m}

I'm not quite sure what is meant by "and the probability \left | \psi_{1}(x) \right |^{2} of finding the particle in dx about x."

Are they literally asking for \left | \psi_{1}(x) \right |^{2}or are they looking for an integral such as:
\int_{x-dx}^{x+dx}\left | \psi_{1}(x^{&#039;}) \right |^{2}dx^{&#039;}

 

[betel]

They are not asking for the integral, (which would be trivial btw), but they want to know the probability of finding the particle around a certain point x in the well.