Heisenberg's uncertainty principle

Nov 2019
2
0
USA
Note: My book presents the Heisenberg's uncertainty principle different from how it usually is presented, presenting it with Δx*Δpₓ≥h/2π, so these problems are designed after that.

My book doesn't either provide answers for multiple choice questions, so I want to check if I'm doing these right or not or if there is something I should add to my answers.

1. The position of an electron is measured within ±Δx. Then the x component of the momentum of that same electron is measured within ±Δpₓ. What can be concluded about the relationship between Δx and Δpₓ?

a) Δx≥h/πΔpₓ
b) Δx≥h/2πΔpₓ
c) Δx≥h/8πΔpₓ
d) Nothing, the Heisenberg uncertainty principle doesn't apply here

For this one I think that the answer is d). The previous question is phrased the same except for the word "Simultaneously" instead of "Then" so I assume that they are measured at different points in time in this question, and from what I've understod is that the principle tells us that both momentum and position can't be known at the same time, so therefor the principle doesn't apply here since momentum is measured afterwards.

2. The position of an electron is measured within ±Δx. Simultaneously, the y component of the momentum of that same electron is measured within ±Δpᵧ. What can be concluded about the relationship between Δx and Δpᵧ?

a) Δx≥h/πΔpᵧ
b) Δx≥h/2πΔpᵧ
c) Δx≥h/8πΔpᵧ
d) Nothing, the Heisenberg uncertainty principle does not apply here.

For this one I am unsure how to think. I haven't seen anything about you being able to combine Δx with Δpᵧ in the formula, but I haven't either seen anything that would say that you can't do it so I can't confirm that it isn't allowed. So, I am thinking that it is either b) or d).

Thank you!
 

topsquark

Forum Staff
Apr 2008
2,978
631
On the dance floor, baby!
1) You are overthinking the language.The intended answer would be b).

2) The answer is d). We can simultaneously measure any two components that aren't the same. So we can measure \(\displaystyle \Delta x\) and \(\displaystyle \Delta p_y\) as accurately as we like.

-Dan