- #1

LagrangeEuler

- 717

- 20

## Homework Statement

Particle is put in into the infinity potential well. How the probability of finding particle between different maxima of probability density is changing by increasing of ##n##?

## Homework Equations

##\psi_n(x)=\sqrt{\frac{2}{a}}\sin \frac{n\pi x}{a}##

##E_n=\frac{n^2\pi^2\hbar^2}{2ma^2}##

## The Attempt at a Solution

##\frac{d}{dx}|\psi_n(x)|^2=\frac{1}{a}\frac{2n\pi}{a}\sin\frac{2n\pi x}{a}=0##

so

##\frac{2n\pi x}{a}=k\pi##

From that ##x=\frac{ka}{2n}##.

To bi maximum

##\cos \frac{2n\pi x}{a}<0##.

Right?

What is easiest way to solve this?