To begin let's use the Wave Packet Explorer program to create wave functions with different uncertainties in momentum.
Use Wave Function Explorer to produce wave functions as shown in Figure1.
(a) (b) (c) (d) (e)
Figure 1: Wave functions with different uncertainties in position.
Compare the result of all groups. Which one needed to include the largest number of momenta?
Which one needed to include the smallest number of momenta?
How is the uncertainty in position related to the uncertainty in momentum?
This exercise indicates that as one of the uncertainties increases the other decreases. This conclusion is built into the wave nature of matter. It does not depend on our measurement instruments. (We have not discussed measurement here - only creating wave functions.)