1. Consider a three dimensional Hilbert space spanned by the orthonomal basis {|1), |2), |3)}. Define two state vectors by |) = b|1) – c[3) and |V) = [c[1) – |2) + c[3)], where b and c are complex constants. (1.1) What is the matrix |)(V |? (1.2) Calculate the inner product (V|¤). (1,3) When |(V)Ð)| takes the maximal value? %3D tiol field
1. Consider a three dimensional Hilbert space spanned by the orthonomal basis {|1), |2), |3)}. Define two state vectors by |) = b|1) – c[3) and |V) = [c[1) – |2) + c[3)], where b and c are complex constants. (1.1) What is the matrix |)(V |? (1.2) Calculate the inner product (V|¤). (1,3) When |(V)Ð)| takes the maximal value? %3D tiol field
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![1. Consider a three dimensional Hilbert space spanned by the orthonomal basis {|1), |2), |3)}. Define two state
vectors by ) = b|1) – c|3) and |V) = [c[1) – |2) + c[3)], where b and c are complex constants.
(1.1) What is the matrix |¤)(V |?
(1.2) Calculate the inner product (V|Ð).
(1.3) When |(V|Ð)| takes the maximal value?
untiol field](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2b1c1b32-0e75-405b-870f-c7d4f0ae8ea0%2F7a5ccfcd-34bc-4ec3-9177-2a056ada60c8%2F9v7zne3_processed.png&w=3840&q=75)
Transcribed Image Text:1. Consider a three dimensional Hilbert space spanned by the orthonomal basis {|1), |2), |3)}. Define two state
vectors by ) = b|1) – c|3) and |V) = [c[1) – |2) + c[3)], where b and c are complex constants.
(1.1) What is the matrix |¤)(V |?
(1.2) Calculate the inner product (V|Ð).
(1.3) When |(V|Ð)| takes the maximal value?
untiol field
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