How is Math Applied in Quantum Physics through Standard Normal Distribution?

[TimeRip496]

∫_-∞^∞(e^{(-x2)/(x₀2)}) dx =π^0.5x₀

How do you get this? Sorry my math sucks.

 

[ShayanJ]

Check here!

 

[mathman]

The standard normal distribution has a density function $f(x)=\frac{1}{\sqrt {2\pi}}e^{-\frac{x^2}{2}}$ with $\int_{-\infty}^{\infty}f(x)dx=1$.

Make the appropriate change of variables and you get the equation you have.