# Regarding the Born approximation

#### Kontilera

Hello!
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,
$$V(r) = \lambda e^{-r^2 / 4a^2}.$$
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 $$ka \ll 1$$?

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#### DrClaude

Mentor
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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