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NeedPhysHelp8
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Hi all,
I was diving into my 3rd year quantum assignment and I saw the following which I have to use for the rest of the question to prove the Cauchy-Schwarz inequality:
|| a|x> + b|y> ||^2
I only really learned a bit about Dirac notation last year, so please let me know if this simplification is right.
( a|x> + b|y> )^{*}( a|x> + b|y> )
a^{*}a<x|x> + a^{*}b<x|y> + b^{*}a<y|x> + b^{*}b<y|y>
Later it says to make substitutions for a= -<x|y> , b= <x|x> to prove the inequality, but I want to make sure I didn't screw up the very first part above...which I have a feeling I did.
Thanks
I was diving into my 3rd year quantum assignment and I saw the following which I have to use for the rest of the question to prove the Cauchy-Schwarz inequality:
Homework Statement
|| a|x> + b|y> ||^2
I only really learned a bit about Dirac notation last year, so please let me know if this simplification is right.
( a|x> + b|y> )^{*}( a|x> + b|y> )
a^{*}a<x|x> + a^{*}b<x|y> + b^{*}a<y|x> + b^{*}b<y|y>
Later it says to make substitutions for a= -<x|y> , b= <x|x> to prove the inequality, but I want to make sure I didn't screw up the very first part above...which I have a feeling I did.
Thanks