Why Are There Two Different Expressions for Uncertainty in Quantum Mechanics?

[Amith2006]

Homework Statement

According to Heisenberg Uncertainty principle,
Del(X)xdel(P) >= h/2(pi)
But there is also another expression given in my book which is,
Del(X)xdel(P) >= h/4(pi)
I asked my lecturer why is it so? She said that, the second expression is obtained from Fourier analysis. But she also said that in calculations, you can use the first one. Which should I use in competitive exams?

Homework Equations

The Attempt at a Solution

 

[swain1]

The second one is the form given in all modern textbooks and the one you will be expected to use in your exams.

 

[da_willem]

In 1D I believe the lower bound on the product of these uncertainties is your second expression.