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gfd43tg
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Homework Statement
Homework Equations
The Attempt at a Solution
Hello,
I just want to make sure I am doing this right
$$<a|b> = a_{x}^{*}b_{x} + a_{y}^{*}b_{y} + a_{z}^{*}b_{z}$$
$$= [(1-i)|x>][-i|x>] + (2 |y>)(-3 |y>) + (0|z>)(|z>)$$
$$=(-i + i^{2})|x> - 6 |y> + 0|z>$$
$$=(-1-i)|x> - 6 |y> $$
Then to find ##\mid<a|b> \mid^{2}##, I need to take the complex conjugate since this is a complex vector
$$\mid<a|b> \mid^{2} = [(-1-i)|x> - 6|y> + 0|z>][(-1+i)|x> - 6|y> + 0|z>]$$
$$= 2|x> + 36 |y> + 0|z>$$
Now I want to make sure that this is even right before I spend time evaluating the other inner products to determine if Schwarz inequality is true.
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