Electron One Split Energy Probability Density Function

[VVS]

Homework Statement

https://www.physicsforums.com/attachment.php?attachmentid=69371&d=1399142463

2. The attempt at a solution
I am working on the last problem now.
Here is what I have got so far. Basically I have converted the coordinate space wave function to a momentum space wave function. Then one can associate an Energy interval to a momentum space interval and integrate the absolute value of momentum space wave function squared in that interval to find the probability density function as a function of Energy. But somehow I am getting a weird result.
View attachment Übung 19.pdf

 

[TSny]

When finding the normalization constant, c, make sure you integrate the square of the magnitude of the wave function.

You are asked to find the probability density for an infinitesimal range E to E + dE. So, you don't need to integrate over an interval.

Your Fourier transform to momentum space looks good to me.

 

[VVS]

Thanks. Yeah you're right about the normalization constant, really sloppy on my side.
Thanks for your hint.