- 3,372
- 465
I have one question... In general I always thought that the exponential function was "dying" out faster than any other polynomial function, such that:
e^{-x} x^a \rightarrow 0 for x \rightarrow \infty.
[eg this is was used quiet commonly and so I got it as a rule-of-thumb, when deriving wavefunctions for a simple example for the Hydrogen atom]
However recently I read in a paper that this is not true, and as an illustration of how can that be, they logarithm-ized the function like:
\ln (e^{-x} x^n) = -x + n \ln x which goes to infinity for x,n\rightarrow \infty.
This I read in here:
http://arxiv.org/pdf/1108.4270v5.pdf
in Sec4 (the new paragraph after Eq4.1)
This has confused me, can someone shred some light?
e^{-x} x^a \rightarrow 0 for x \rightarrow \infty.
[eg this is was used quiet commonly and so I got it as a rule-of-thumb, when deriving wavefunctions for a simple example for the Hydrogen atom]
However recently I read in a paper that this is not true, and as an illustration of how can that be, they logarithm-ized the function like:
\ln (e^{-x} x^n) = -x + n \ln x which goes to infinity for x,n\rightarrow \infty.
This I read in here:
http://arxiv.org/pdf/1108.4270v5.pdf
in Sec4 (the new paragraph after Eq4.1)
This has confused me, can someone shred some light?