Question

Which of the following are valid regarding the Uncertainty Principle? If a statement is invalid, write a brief statement indicating why.

(a) It states that you cannot simultaneously measure both the position and momentum of a particle to infinite precision.

(b) It arises from the wave nature of particles.

(c) If the uncertainty in a particle’s momentum is determined to be ∆p, then the maximum uncertainty in its position must be ∆x = ~ 2∆p .

(d) It implies that if a particle decays in a certain time ∆t, then there is a minimum uncertainty in its energy.

Answer 1

(a) Valid

(b) Valid

(c) Invalid; because if uncertainty in momentum is dP ie., it has been determined precisely. Then uncertainty in position of particle must be infinite but here given that it is equal to 2dP, which is wrong.

(d) Invalid; Here nothing can be said about uncertainty in energy of particle if it decays in time dt. We can only have heisenberg's mathematical relationship between these two.