Regarding the Born approximation

  • Thread starter Kontilera
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In order to prepare for an exam I have started solving exercies problems and have gotten most of them right but have quetion a regarding a solution.

In this probelm I used the first order Born approximation in order to calculate the differential and total cross section for the potential,
[tex] V(r) = \lambda e^{-r^2 / 4a^2}. [/tex]
Now, how can I see the limits of this approximation? E.g. can we see if it is valid for a particle with a given mass assuming that we have [tex]ka \ll 1[/tex]?


The criterion for the validity of the Born approximation is
\frac{m | V_0 | a^2}{\hbar^2} \ll 1
where ##m## is the mass of the particle, ##V_0## and ##a## the height and range of the potential, respectively.

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