- #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?