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Proof of Cauchy-Schwarty Inequality

  1. Apr 22, 2015 #1
    Proof of Cauchy-Schwarty Inequality from the Book "Quantum Mechanics Demystified" Page 133.
    I do not understand one key step! Most appreciated someone could help.
    Please see attached file.
     

    Attached Files:

  2. jcsd
  3. Apr 22, 2015 #2
    Hello Peter,

    That step is kind of like taking the inner product of f with f. To put it into perspective, if we take an expression (a+b) squared, we would get a^2 + 2ab + b^2. Same concept here from what I see.

    elite
     
  4. Apr 22, 2015 #3
    Hi Elite,
    Many thank! I still cannot understand.
    Perhaps this can help:
    If : | f > = |a > - < b | a> ( | b >)
    Then: < f | = ??
     
  5. Apr 22, 2015 #4

    stevendaryl

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    It looks like a typo. I think the author meant to write:
    [itex]|f\rangle = |\phi\rangle - \dfrac{\langle \psi|\phi\rangle}{\langle \psi|\psi \rangle} |\psi\rangle[/itex]
     
  6. Apr 22, 2015 #5
    Hi Steven,
    Thank you. You are smart! I think you are right!
    By the way, how do you input your equation in the above message? I cannot input the equation using the key board.
     
  7. Apr 22, 2015 #6

    stevendaryl

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    You have to write it using LaTex, which uses syntax like

    \psi^*

    for [itex]\psi^*[/itex]

    Alternatively, you can write most things using the symbols provided at the top of the edit window (click on Σ).
     
  8. Apr 22, 2015 #7
    Hi Steven,
    I do not know the Latex code.
    Can you write a fraction (in your equation) by using the edit window bar? And how can use the X squared icon in the edit window bar?
    Thanks
     
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