(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

An electron is confined to the region of the x axis between x = 0 and x = L (where L = 1nm). Given a staten= 3, find the location of the points in the box at which the probability of finding the electron is half it's maximum value

2. Relevant equations

[tex]\psi^2(x)=\frac{2}{L}\sin^2\left(\frac{n\pi x}{L}\right)[/tex]

3. The attempt at a solution

I understand that the wavefunction squared (above) gives the probability at location x, and its integration gives the probability over set regions between x = 0 and x =l. However, the only way I can see of finding x from a given probability is to assume:

[tex]\psi^2(x)=0.5[/tex]

and try to manipulate the equation to give it in terms of x. Is this the right method? If so, how do I take out the sine term?

Cheers

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# 1D Particle in a box - locations at set probability

**Physics Forums | Science Articles, Homework Help, Discussion**