For a given state |) and Hermitian operators A, B, (a) prove that AT)= (A))AA|4), (2) where we used the same notation in class for the expectation and tha variance of the operator A and is some state orthogonal to |) (b) Use this results to rederive then (square root of the) general uncertainty relation we derived in class, AAÄB > GK[A, B]}|. (3)
For a given state |) and Hermitian operators A, B, (a) prove that AT)= (A))AA|4), (2) where we used the same notation in class for the expectation and tha variance of the operator A and is some state orthogonal to |) (b) Use this results to rederive then (square root of the) general uncertainty relation we derived in class, AAÄB > GK[A, B]}|. (3)
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Transcribed Image Text:For a given state |) and Hermitian operators A, B, (a) prove that
AT)= (A))AA|4),
(2)
![where we used the same notation in class for the expectation and tha variance of the operator A
and is some state orthogonal to |)
(b) Use this results to rederive then (square root of the) general uncertainty relation we derived in
class,
AAÄB > GK[A, B]}|.
(3)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff9faf22f-10a8-4cb5-bec9-d63452f6293a%2F5c90e389-286a-458d-97f5-287db345c591%2F9ehhrof.png&w=3840&q=75)
Transcribed Image Text:where we used the same notation in class for the expectation and tha variance of the operator A
and is some state orthogonal to |)
(b) Use this results to rederive then (square root of the) general uncertainty relation we derived in
class,
AAÄB > GK[A, B]}|.
(3)
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