-2
$\begingroup$

A particle is confined in a one dimensional box of length $a$.

What is the probability of finding the particle at $x = a/4$?

I know that the wave function is written as

$$y= A\sin([(\pi x)/a]$$ where $x$ is from 0 to $a$.

After normalization, I found that $$A = \sqrt{\frac{2}{a}},$$ so $$y= \sqrt{\frac{2}{a}}\sin\left(\frac{\pi x}{a}\right)$$

I know to find the probability of a region $(a,b)$ I need to integrate from $a$ to $b$ over the probability density. However I don't know how to find the probability at a specific point (i.e. $x=a/4$).

$\endgroup$

closed as off-topic by ZeroTheHero, Kyle Kanos, Aaron Stevens, Buzz, John Rennie Feb 3 at 6:51

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "Homework-like questions should ask about a specific physics concept and show some effort to work through the problem. We want our questions to be useful to the broader community, and to future users. See our meta site for more guidance on how to edit your question to make it better" – ZeroTheHero, Kyle Kanos, Aaron Stevens, Buzz, John Rennie
If this question can be reworded to fit the rules in the help center, please edit the question.

  • 1
    $\begingroup$ would the probability of a specific point equal to 0? $\endgroup$ – Daniel Vo Feb 2 at 21:52
  • 1
    $\begingroup$ Yes, if the distribution function is assumed to be continuous. Which in this case it is... $\endgroup$ – LordVader007 Feb 2 at 22:00
2
$\begingroup$

As with any continuous probability distribution, the probability of finding the particle at any specific point is equal to zero.

Luckily that's not a real problem, because the best any physical experiment can do is to find (or fail to find) the particle in some finite region of space.

$\endgroup$

Not the answer you're looking for? Browse other questions tagged or ask your own question.