Unformatted text preview: rootmeansquare deviation from the mean ( i.e. standard deviation ). Note that this corresponds to a lower limit. It is always possible to know things less well. Uncertainty as a Function of Time: If at t = 0 we have localized the particle to within ∆ x , then at t = 0 ∆ p x ≈ h/ ∆ x and ∆ v x ≈ h/(m ∆ x ) . At a later time t, ∆ x = ∆ v x t ≈ ht/(m ∆ x ) and hence, 1. The better we know the particle’s position at t = 0 ( i.e. smaller ∆ x ), the worse we know it’s position at a later time t ( i.e. larger ∆ x ). 2. The uncertainty in the particle’s position ∆ x increases with time. In classical physics you can know precisely the position and momentum of a particle ( i.e. no limit on the precision). Furthermore, if you know the position and momentum of an isolated particle at t = 0, then the exact position of the particle can be predicted for all future times!...
View
Full Document
 Spring '07
 FIELDS
 Physics, mechanics, Energy, Momentum, Heisenberg Uncertainty Principle, Uncertainty Principle, Exact Uncertainty Relations

Click to edit the document details