Comparison of width of a wavefunction in real space and momentum space

by BasharTeg
Tags: comparison, momentum, real, space, wavefunction, width
 P: 5 Hello, I have a slight problem with Quantumtheory here. 1. The problem statement, all variables and given/known data I have solved the schrödinger equation in the momentum space for a delta potential and also transfered it into real space. So now I have to find the correlation between the width of the wavefunction in both spaces (and then motivate it physically) and I am stuck here because I don't even know where to start. 2. Relevant equations $\Psi (x) = \sqrt{\kappa}e^{- \kappa |x|}$ $\Psi (p) = \frac{\sqrt{2 ( \hbar \kappa)^3}}{\sqrt{\pi}(p^2 + (\hbar \kappa)^2)}$ 3. The attempt at a solution I was thinking about maybe the uncertainty relation of momentum and space would help here, but I am stuck where to start. Hope someone can help or give a hint.
 Emeritus Sci Advisor HW Helper Thanks PF Gold P: 11,869 Just looking at the functions, you can approximate the characteristic width of the wave functions in position space by using $\kappa x \approx 1$ and in momentum space by using $p / \hbar \kappa \approx 1$. If you want to be more precise, calculate $\Delta x = \sqrt{\langle x^2 \rangle - \langle x \rangle^2}$ and $\Delta p = \sqrt{\langle p^2 \rangle - \langle p \rangle^2}$.