Question

Derive the constant A for a normalized one-dimensional Maxwellian distribution with variation from – infinity to + infinity.
F(u)= Ae-mu2/kT

Answer 1

$$a=\frac{m}{kT}$$

$$F(u)=Ae^{-0.5au^2}$$

$$\int_{-\infty}^{\infty}Ae^{-0.5au^2}du=1$$

$$\int_{-\infty}^{\infty}e^{-0.5au^2}du=\sqrt{\frac{2\pi}{a}}$$

Thus,

$$A=\sqrt{\frac{m}{2\pi kT}}$$