Probability of finding a particle in a 1-D box max. at centre?

[Apashanka]

TL;DR

Probability density $(2/L)*sin^2(\pi x/L)$

From the probability density plot why it is max at the centre of the box...e.g probability to find the particle per unit le gth is max. at the centre of the box??why not at any other position??

 

[anuttarasammyak]

You say about the ground state n=1. As for excited states for larger n you will see almost homogeneous distribution as you may expect.