Proof of Cauchy-Schwarty Inequality

[Peter Yu]

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.

 

[elitewarr]

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

 

[Peter Yu]

Hi Elite,
Many thank! I still cannot understand.
Perhaps this can help:
If : | f > = |a > - < b | a> ( | b >)
Then: < f | = ??

 

[stevendaryl]

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.

It looks like a typo. I think the author meant to write:
$|f\rangle = |\phi\rangle - \dfrac{\langle \psi|\phi\rangle}{\langle \psi|\psi \rangle} |\psi\rangle$

 

[Peter Yu]

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.

 

[stevendaryl]

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.

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

\psi^*

for $\psi^*$

Alternatively, you can write most things using the symbols provided at the top of the edit window (click on Σ).

 

[Peter Yu]

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