# 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 $$ka \ll 1$$?

Related Quantum Physics News on Phys.org

#### 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.

"Regarding the Born approximation"

### Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving