What happens to the momentum uncertainty as the position uncertainty approaches zero?

Question

228 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-10-01T17:28:29

#DeltaxDeltap_x >= ℏ//2#

where #Deltax# indicates the uncertainty of position and #Deltap_x# indicates uncertainty of momentum...

...you can see that if you want to maintain the inequality, if #Deltax# is small, #Deltap_x# has to be large enough that #DeltaxDeltap_x >= ℏ//2#.

And so, as #Deltax -> 0#, it must be that #Deltap_x -> oo# so that #DeltaxDeltap_x# is not only positive, but greater than the small constant #ℏ//2#.