- #1
Nykrus
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Homework Statement
An electron is confined to the region of the x-axis between x = 0 and x = L (where L = 1nm). Given a state n = 3, find the location of the points in the box at which the probability of finding the electron is half it's maximum value
Homework Equations
[tex]\psi^2(x)=\frac{2}{L}\sin^2\left(\frac{n\pi x}{L}\right)[/tex]
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