1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Measuring Energy and Linear Momentum Consecutively

  1. Jun 25, 2008 #1
    Can the total energy and linear momentum of a particle moving in one dimension in a constant potential field be measured consecutively with no uncertainty in the values obtained?

    Yes, this is possible. The energy and linear momentum operators are, respectively

    [tex]\hat{H} = -\frac{\hbar^2}{2m}\frac{\partial^2}{\partial x^2} + V[/tex]

    [tex]\hat{p} = -i\hbar\frac{\partial}{\partial x}[/tex]

    Now, note that these two operators commute. Because of this, they share the same eigenstates. Now, once the total energy or linear momentum is measured, the wavefunction of the state collapses into an eigenstate of the measured observable. Now, this eigenstate is also an eigenstate of the observable which hasn't been measured yet. Therefore, we can precisely measure this unmeasured observable as well. [tex]\blacksquare[/tex]

    Are my arguments correct?
  2. jcsd
  3. Jun 25, 2008 #2


    User Avatar
    Homework Helper
    Gold Member

    You can also directly tell from the fact that the energy in a constant potential field is a function of momentum only. If you've measured momentum, you know the energy too. And yes, your argument is correct.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook