# Probability of WaveFunction [closed]

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. $$x=a/4$$).

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

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