Question

Obtain an expression of probability for finding the free particle at position x
confined in a box of length a.

Answer 1

The normalized wavefunction for a free particle found at $x$ in a 1-dimensional box of length $a$ can be found from Schrödinger equation:

$$\psi=\sqrt{\frac{2}{a}}\text{sin}\frac{n\pi}{a}x.$$