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!

Quantum question

  1. Jan 12, 2006 #1


    User Avatar

    I have a question... if anyone can maybe help :confused:

    you have psi = a(psi1) + b(psi2) + c(psi3) and the state is orthonormal...
    what is the expectation value of O if O (O is an operator) yields known eigenvalues for psi1 psi2 and psi3 i tried to say that psi1*Opsi1 over all space is (a)(eigenvalue of psi1) times integral of psi1*psi1 which is 1 since the state is orthonormal but that didn't give me the right answer. The correct answer is 1 with a= 1/(root(6)) b= 1/(root(2)) c= 1/(root(3)) and Opsi1 = 1psi1, Opsi2 = -1psi2, Opsi3 = 2psi3 any help would be greatly appreciated :biggrin:

    Last edited: Jan 12, 2006
  2. jcsd
  3. Jan 12, 2006 #2
    I get 1/3 as follows:

    [itex]<O> = <\psi|O|\psi>[/itex]
    [itex] = <a\psi_1 + b\psi_2 + c\psi_3|O|a\psi_1 + b\psi_2 + c\psi_3>[/itex]
    [itex] = <a\psi_1 + b\psi_2 + c\psi_3|a\psi_1 - b\psi_2 + 2c\psi_3>[/itex]
    [itex] = a^2 - b^2 + 2c^2[/itex]
    [itex] = \frac{1}{6} - \frac{1}{2} + \frac{2}{3}[/itex]
    [itex] = \frac{1}{3}[/itex]
    Last edited: Jan 12, 2006
  4. Jan 12, 2006 #3


    User Avatar

    hey thank you very much :) you are correct but the answer is 1 because i switched Opsi1 and Opsi2 Opsi1= -1psi1 and Opsi2= 1psi2 so it is -1/6+ 1/2+ 2/3 = 1 thank you again :)
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Quantum question
  1. Quantum question (Replies: 2)

  2. Quantum Cat question (Replies: 51)