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Unformatted text preview: 2 ) = 1 2 + 1 2 cos = 1 2 + 1 2 cos( 2 + ) = 1 21 2 sin . (2) For the negative channel, the probability is P ( ) = sin 2 ( 2 ) = 1 21 2 cos = 1 21 2 cos( 2 + ) = 1 2 + 1 2 sin . (3) Q5B.10 To normalize a complex vector  i , the inner product of the vector with itself must equal unity. Thus, for general  i we require h  i = 1 2 * 1 2 = ( 1 ) * ( 1 ) + ( 2 ) * ( 2 ) =  1  2 +  2  2 = 1 . (4) a) For  i = a2 ia we have h  i =  a  2 +  2 ia  2 = a 2 + 4 a 2 = 5 a 2 = 1, requiring a = 1 5 b) For  i = a (1 + i ) ai we have h  i =  a (1 + i )  2 +  ai  2 = ( a 2 + a 2 ) + a 2 = 3 a 2 = 1, requiring a = 1 3 c) For  i = a e i a ei we have h  i =  a e i  2 +  a ei  2 = a 2 + a 2 = 2 a 2 = 1, requiring a = 1 2 In the above normalization procedure, we take the positive square root by convention. 1...
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 Spring '11
 EricSzarmes
 Physics, Work

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