- #1

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[tex]\psi_{1}(x)[/tex]

(how many nodes are there in the ground state?) and the probability

[tex]\left | \psi_{1}(x) \right |^{2}[/tex]

of finding the particle in dx about x.

[tex] V(x)=\begin{cases}

& \infty,\text{ }x \geq a, x\leq -a \\

& 0,\text{ } -a< x< a

\end{cases} [/tex]

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

[tex]\psi_{1}(x)=\sqrt{\frac{1}{a}}sin(\frac{\pi}{a}x)[/tex]

[tex]E_{1}=\frac{\hbar^{2}\pi^{2}}{2m}[/tex]

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

Are they literally asking for [tex]\left | \psi_{1}(x) \right |^{2}[/tex]or are they looking for an integral such as:

[tex]\int_{x-dx}^{x+dx}\left | \psi_{1}(x^{'}) \right |^{2}dx^{'}[/tex]