Coordinate space and momentum space

[Felicity]

Homework Statement

given A(k)=N/(k²+a²) calculate psi(x) and show that

(delta k * delta x) > 1

independent of the choice of a

The Attempt at a Solution

I calculated psi(x) to be (N*pi/a)*e^-|ax|

Would it be ok to compute <x> and <x²> in coordinate space and <k> and <k²> in momentum space (which gives me simple multiplication for all my operators) and then find (delta x * delta k) using

delta x = sqrt(<(x-<x>)>) and delta k = sqrt(<(k-<k>)>) ?

do i have to transform anything before I do this? How would I do that?

Thank you

 

[Jhero]

for your post! It seems like you are on the right track with calculating psi(x) and using the operators to find (delta x * delta k). To show that (delta k * delta x) > 1, you can use the uncertainty principle, which states that (delta x * delta k) >= hbar/2, where hbar is the reduced Planck's constant. Since hbar/2 is a positive constant, this means that (delta x * delta k) > 1 regardless of the choice of a. Therefore, your calculations should be correct and no further transformations are needed. Keep up the good work!