Question

Calculate the probability of finding the particle in a one dimensional box of width

L, in state n within the intervals[0,L/4]

Answer 1

The probability function is

$$\Psi_m=\sqrt{\dfrac{2}{l}} \sin\bigg(\dfrac{n\pi x}{l}\bigg),\\\space\\ \Psi_m=\sqrt{\dfrac{2}{L}} \sin\bigg(\dfrac{n\pi (L/4)}{L}\bigg)=\sqrt{\dfrac{2}{L}} \sin\bigg(\dfrac{n\pi}{4}\bigg).$$