How Do You Differentiate V(αr) = α^n V(r) with Respect to α?

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Hello every body,

can you help me in solving these quantum mechanics problems?

http://www.itap.physik.uni-stuttgart.de/lehre/vorlesungen/advqm2008/assign09.pdf"



Thanks,
 
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Hi abeedo! :smile:

Show us what you've tried, and where you're stuck, and then we'll know how to help.

Start with Problem 1(a) and (b). :smile:
 
Hello Tiny-tim:)


Actually, my pen has been frozen when it met the paper:)

I have searched through 6 books in quantum mechanics , and nothing helps except (c) from problem 1...
 
Let's start with 1a. Has nothing to do with physics.

Differentiate V\left(\alpha \vec{r}\right) = \alpha^n V\left(\vec{r}\right) wrt 'alpha'.
 
To solve this, I first used the units to work out that a= m* a/m, i.e. t=z/λ. This would allow you to determine the time duration within an interval section by section and then add this to the previous ones to obtain the age of the respective layer. However, this would require a constant thickness per year for each interval. However, since this is most likely not the case, my next consideration was that the age must be the integral of a 1/λ(z) function, which I cannot model.
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