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Quantum question

  1. Jan 12, 2006 #1

    qtp

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    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:

    qtP
     
    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

    qtp

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    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 :)
     
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