Infinite square well. probability isues.

  • Thread starter OGrowli
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  • #1
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(a) Obtain the ground state wave function and energy. Draw the wave function
[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]
 

Answers and Replies

  • #2
318
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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.
 

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