1. Not finding help here? Sign up for a free 30min 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!

Violation of the laws of quantum physics?

  1. Nov 14, 2008 #1
    If I want to calculate <x> of an electron that is in a state described by [tex]\psi (x,t)=\frac{1}{\sqrt{2}}[\psi_{0}(x,t) + \psi_{1}(x,t)]][/tex] where [tex]\psi_{0} [/tex] and [tex]\psi_{1}[/tex] are the two lowest energy states of an electron in a one dimensional box, can I then simply calculate <x> for [tex]\frac{1}{\sqrt{2}}\psi_{0}[/tex] and [tex]\frac{1}{\sqrt{2}}\psi_{1}[/tex] alone and add them?

    Is it even possible for an electron to have this energy? Doesn't it violate the laws of quantum physics? I find it strange that this was an exam problem in quantum physics at my university recently.
    Last edited: Nov 14, 2008
  2. jcsd
  3. Nov 14, 2008 #2
    You know, what <x> means?
    It is [tex]\langle x\rangle=\frac12\int_{-\infty}^{\infty}dx x (\psi_0^2+\psi_1^2+2\psi_0\psi_1)[/tex].
    Indeed, [tex]\int_{-\infty}^{\infty}dx 2\psi_0\psi_1=0[/tex]
    but [tex]\int_{-\infty}^{\infty}dx 2x\psi_0\psi_1\neq0[/tex].
    So you can't calculate <x> for $\psi_0$ and $\psi_1$ separately.
    Sure, it's a legal state in quantum physics.

  4. Nov 14, 2008 #3
    The energy must still be either E0 or E1, right?
  5. Nov 14, 2008 #4
    If you measure the energy, you will find either E0 or E1. And that is the special property of quantum mechanics, that the probability is for either case 50%.
  6. Nov 14, 2008 #5
    But it's not possible to measure E with certainty, right?

    And the [tex]\frac{1}{\sqrt{2}}[/tex] is there just to normalise the probability function?
  7. Nov 14, 2008 #6
    Given your other post about <p>, first read your textbook!
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Violation of the laws of quantum physics?
  1. Quantum Physics (Replies: 1)

  2. Quantum Physics (Replies: 2)

  3. Quantum physics (Replies: 0)